Bernd Flemisch committed Oct 07, 2019 1 This tutorial is similar to tests/porousmediumflow/2p/adaptive and restricted to the cell-centered finite volume TPFA discretization scheme.  Sina Ackermann committed Oct 07, 2019 2 You need [ALUGrid][0] in order to compile and run it.  Sina Ackermann committed Oct 07, 2019 3 4 5 6  # Two-phase flow with infiltration and adaptive grid ## Problem set-up  Bernd Flemisch committed Oct 07, 2019 7 8 9 10 In this example we model a soil contamination problem where DNAPL infiltrates a porous medium. The initial distribution of DNAPL is known and we can read it from a txt-file. To describe that problem we use a two phase model of two immiscible fluids with the multiphase Darcy's law as the description of momentum, i.e.:  Farid Mohammadi committed Oct 07, 2019 11 math  Bernd Flemisch committed Oct 07, 2019 12 13  v_\alpha = - \frac{k_{r\alpha}}{\mu_\alpha} \textbf{K} \left(\textbf{grad}\, p_\alpha - \varrho_{\alpha} {\textbf g} \right)  Farid Mohammadi committed Oct 07, 2019 14   Bernd Flemisch committed Oct 07, 2019 15 16 17  If we insert this into the conservation equations for each phase $$\alpha$$ that leads to:  Farid Mohammadi committed Oct 07, 2019 18 math  Bernd Flemisch committed Oct 07, 2019 19 \phi \frac{\partial \varrho_\alpha S_\alpha}{\partial t}  Farid Mohammadi committed Oct 07, 2019 20  -\textbf{div} \left\{ \varrho_\alpha \frac{k_{r\alpha}}{\mu_\alpha} \mathbf{K} \left(\textbf{grad}\, p_\alpha - \varrho_{\alpha} \bf g \right)  Bernd Flemisch committed Oct 07, 2019 21  \right\} - q_\alpha = 0  Farid Mohammadi committed Oct 07, 2019 22   Bernd Flemisch committed Oct 07, 2019 23   Farid Mohammadi committed Oct 07, 2019 24 To reduce the number of unknowns and close the system we need closure relations for this equations. For that, we make use of a $p_c - S_w$ as well as a $k_r - S_w$ - relationship. In this problem we use a Van-Genuchten parameterization. The parameters for that relationship are specified in the spatialparams.hh file.  Bernd Flemisch committed Oct 07, 2019 25 26  With the additional constraint that $S_w + S_n = 1$ we reduce the number of primary variables to two.  Farid Mohammadi committed Oct 07, 2019 27 In this example we use the wetting phase pressure $p_0$ and the saturation of the non-wetting phase $S_1$ as primary variables. It is also possible to switch that formulation to the non-wetting pressure and the wetting saturation.  Bernd Flemisch committed Oct 07, 2019 28 29 30 31  The two-dimensional model domain is 6m x 4m and contains a lens with a lower permeability and porosity. We read the initial values for the DNAPL saturation and the water pressure from a file. The lens and the initial saturation can be seen in Figures 1 and 2.  Farid Mohammadi committed Oct 07, 2019 32 ![](./img/test_2p_pointsource_lens.png)  Bernd Flemisch committed Oct 07, 2019 33   Farid Mohammadi committed Oct 07, 2019 34 ![](./img/test_2p_pointsource_initial.png)  Bernd Flemisch committed Oct 07, 2019 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68  At the left and the right boundary of the domain we set a linear pressure gradient as a Dirichlet boundary condition. On the upper and lower boundary we set Neumann boundary conditions. DNAPL enters the model domain at the upper boundary between 1.75m ≤ x ≤ 2m with a rate of 0.04 kg/ms. That means that we set the value for the Neumann boundary flux to that rate in between 1.75m and 2m. On the rest of the Neumann boundary we set the flux to zero, which means we define it as a no-flow boundary. In addition, the DNAPL is injected at a point source at x = 0.502 and y = 3.02 with a rate of 0.1 kg/s. ## Discretization We descritize the equations with a cell-centered finete volume TPFA scheme in space and an implicit Euler scheme in time. We use Newton's method to solve the system of nonlinear equations. For more information about the discretization please have a look at the handbook. ## Adaptive grid The grid is adapitvely refined around the injection. The adaptive behaviour can be changed with input parameters in the params.input file. [0]: https://gitlab.dune-project.org/extensions/dune-alugrid ## The file spatialparams.hh we include the basic spatial parameters for finite volumes file from which we will inherit cpp #include  we include all laws which are needed to define the interaction between the solid matrix and the fluids, e.g. laws for capillary pressure saturation relationships. cpp #include #include namespace Dumux {  In the TwoPTestSpatialParams class we define all functions needed to describe the porous matrix, e.g. defines porosity and permeability cpp template class TwoPTestSpatialParams : public FVSpatialParams>  Martin Utz committed Oct 07, 2019 69 70 {   Bernd Flemisch committed Oct 07, 2019 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 we introduce using declarations that are derived from the property system which we need in this class cpp using GridView = typename FVGridGeometry::GridView; using Element = typename GridView::template Codim<0>::Entity; using FVElementGeometry = typename FVGridGeometry::LocalView; using SubControlVolume = typename FVElementGeometry::SubControlVolume; using ThisType = TwoPTestSpatialParams; using ParentType = FVSpatialParams; static constexpr int dimWorld = GridView::dimensionworld; using GlobalPosition = typename Element::Geometry::GlobalCoordinate; using EffectiveLaw = RegularizedVanGenuchten; public: using MaterialLaw = EffToAbsLaw; using MaterialLawParams = typename MaterialLaw::Params; using PermeabilityType = Scalar;  Sina Ackermann committed Oct 07, 2019 89   Bernd Flemisch committed Oct 07, 2019 90 91 92  TwoPTestSpatialParams(std::shared_ptr fvGridGeometry) : ParentType(fvGridGeometry) {  Martin Utz committed Oct 07, 2019 93   Bernd Flemisch committed Oct 07, 2019 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 we get the position of the lens from the params.input file. The lens is defined by the position of the lower left and the upper right corner cpp lensLowerLeft_ = getParam("SpatialParams.LensLowerLeft"); lensUpperRight_ = getParam("SpatialParams.LensUpperRight");  we set the parameters for the material law (here Van-Genuchten Law). First we set the residual saturations for the wetting phase and the non-wetting phase. lensMaterialParams_ are the material parameters define the material parameters for the lens while outerMaterialParams_ define material marams for the rest of the domain cpp lensMaterialParams_.setSwr(0.18); lensMaterialParams_.setSnr(0.0); outerMaterialParams_.setSwr(0.05); outerMaterialParams_.setSnr(0.0);  we set the parameters for the Van Genuchten law alpha and n cpp lensMaterialParams_.setVgAlpha(0.00045); lensMaterialParams_.setVgn(7.3); outerMaterialParams_.setVgAlpha(0.0037); outerMaterialParams_.setVgn(4.7);  here we get the permeabilities from the params.input file. In case that no parameter is set, the default parameters (9.05e-12 and 4.6e-10) are used cpp lensK_ = getParam("SpatialParams.lensK", 9.05e-12); outerK_ = getParam("SpatialParams.outerK", 4.6e-10); }  We define the (intrinsic) permeability \f$[m^2]\f$. In this test, we use element-wise distributed permeabilities. cpp template PermeabilityType permeability(const Element& element, const SubControlVolume& scv, const ElementSolution& elemSol) const { if (isInLens_(element.geometry().center())) return lensK_; return outerK_; }  We set the porosity \f$[-]\f$ depending on the position cpp Scalar porosityAtPos(const GlobalPosition& globalPos) const { if (isInLens_(globalPos)) return 0.2; return 0.4; }  We set the parameter object for the Van Genuchten material law. cpp template const MaterialLawParams& materialLawParams(const Element& element, const SubControlVolume& scv, const ElementSolution& elemSol) const { if (isInLens_(element.geometry().center())) return lensMaterialParams_; return outerMaterialParams_; }  Here we can define which phase is to be considered as the wetting phase. Here the wetting phase is the the first phase of the fluidsystem. In this case that is water. cpp template int wettingPhaseAtPos(const GlobalPosition& globalPos) const { return FluidSystem::phase0Idx; } private:  we have a convenience definition of the position of the lens cpp bool isInLens_(const GlobalPosition &globalPos) const { for (int i = 0; i < dimWorld; ++i) { if (globalPos[i] < lensLowerLeft_[i] + eps_ || globalPos[i] > lensUpperRight_[i] - eps_) return false; } return true; } GlobalPosition lensLowerLeft_; GlobalPosition lensUpperRight_; Scalar lensK_; Scalar outerK_; MaterialLawParams lensMaterialParams_; MaterialLawParams outerMaterialParams_; static constexpr Scalar eps_ = 1.5e-7; }; } // end namespace Dumux  ## The file problem.hh ## Include files The cell centered, two-point-flux discretization scheme is included: cpp #include  The fluid properties are specified in the following headers: cpp #include #include #include #include  This is the porous medium problem class that this class is derived from: cpp #include  The two-phase flow model is included: cpp #include  The local residual for incompressible flow is included: cpp #include  We include the header that specifies all spatially variable parameters: cpp #include "spatialparams.hh"  A container to read values for the initial condition is included: cpp #include  ## Define basic properties for our simulation We enter the namespace Dumux. All Dumux functions and classes are in a namespace Dumux, to make sure they don't clash with symbols from other libraries you may want to use in conjunction with Dumux. One could use these functions and classes by prefixing every use of these names by ::, but that would quickly become cumbersome and annoying. Rather, we simply import the entire Dumux namespace for general use: cpp namespace Dumux {  The problem class is forward declared: cpp template class PointSourceProblem;  We enter the namespace Properties, which is a sub-namespace of the namespace Dumux: cpp namespace Properties {  A TypeTag for our simulation is created which inherits from the two-phase flow model and the cell centered, two-point-flux discretization scheme. cpp namespace TTag { struct PointSourceExample { using InheritsFrom = std::tuple; }; }  We use non-conforming refinement in our simulation: cpp template struct Grid { using type = Dune::ALUGrid<2, 2, Dune::cube, Dune::nonconforming>; };  The problem class specifies initial and boundary conditions: cpp template struct Problem { using type = PointSourceProblem; };  The local residual contains analytic derivative methods for incompressible flow: cpp template struct LocalResidual { using type = TwoPIncompressibleLocalResidual; };  In the following we define our fluid properties. cpp template struct FluidSystem {  We define a convenient shortcut to the property Scalar: cpp using Scalar = GetPropType;  First, we create a fluid system that consists of one liquid water phase. We use the simple description of water, which means we do not use tabulated values but more general equations of state. cpp using WettingPhase = FluidSystems::OnePLiquid >;  Second, we create another fluid system consisting of a liquid phase as well, the Trichlorethene (DNAPL) phase: cpp using NonwettingPhase = FluidSystems::OnePLiquid >;  Third, we combine both fluid systems in our final fluid system which consist of two immiscible liquid phases: cpp using type = FluidSystems::TwoPImmiscible; };  we set the formulation for the primary variables to p0s1. In this case that means that the water pressure and the DNAPL saturation are our primary variables. cpp template struct Formulation { static constexpr auto value = TwoPFormulation::p0s1; };  We define the spatial parameters for our simulation: cpp template struct SpatialParams {  We define convenient shortcuts to the properties FVGridGeometry and Scalar: cpp private: using FVGridGeometry = GetPropType; using Scalar = GetPropType;  Finally we set the spatial parameters: cpp public: using type = TwoPTestSpatialParams; };  We enable caching for the grid volume variables, the grid flux variables and the FV grid geometry. The cache stores values that were already calculated for later usage. This makes the simulation faster. cpp template struct EnableGridVolumeVariablesCache { static constexpr bool value = false; }; template struct EnableGridFluxVariablesCache { static constexpr bool value = false; }; template struct EnableFVGridGeometryCache { static constexpr bool value = false; };  We leave the namespace Properties. cpp }  ## The problem class We enter the problem class where all necessary boundary conditions and initial conditions are set for our simulation. As this is a porous medium problem, we inherit from the basic PorousMediumFlowProblem. cpp template class PointSourceProblem : public PorousMediumFlowProblem {  We use convenient declarations that we derive from the property system. cpp using ParentType = PorousMediumFlowProblem; using GridView = GetPropType; using Element = typename GridView::template Codim<0>::Entity; using Vertex = typename GridView::template Codim::Entity; using Scalar = GetPropType; using FluidSystem = GetPropType; using PrimaryVariables = GetPropType; using FVGridGeometry = GetPropType; using PointSource = GetPropType; using BoundaryTypes = GetPropType; using GlobalPosition = typename Element::Geometry::GlobalCoordinate; using NumEqVector = GetPropType; using Indices = typename GetPropType::Indices;  We define some indices for convenient use in the problem class: cpp enum { pressureH2OIdx = Indices::pressureIdx, saturationDNAPLIdx = Indices::saturationIdx, contiDNAPLEqIdx = Indices::conti0EqIdx + FluidSystem::comp1Idx, waterPhaseIdx = FluidSystem::phase0Idx, dnaplPhaseIdx = FluidSystem::phase1Idx }; public:  This is the constructor of our problem class: cpp PointSourceProblem(std::shared_ptr fvGridGeometry) : ParentType(fvGridGeometry) {  We read in the values for the initial condition of our simulation: cpp initialValues_ = readFileToContainer>("initialsolutioncc.txt"); }  First, we define the type of boundary conditions depending on location. Two types of boundary conditions can be specified: Dirichlet or Neumann boundary condition. On a Dirichlet boundary, the values of the primary variables need to be fixed. On a Neumann boundary condition, values for derivatives need to be fixed. Mixed boundary conditions (different types for different equations on the same boundary) are not accepted. cpp BoundaryTypes boundaryTypesAtPos(const GlobalPosition &globalPos) const { BoundaryTypes values;  We specify Dirichlet boundaries on the left and right hand side of our domain: cpp if (onLeftBoundary_(globalPos) || onRightBoundary_(globalPos)) values.setAllDirichlet(); else  The top and bottom of our domain are Neumann boundaries: cpp values.setAllNeumann(); return values; }  Second, we specify the values for the Dirichlet boundaries, depending on location. As mentioned, we need to fix values of our two primary variables: the water pressure and the Trichlorethene saturation. cpp PrimaryVariables dirichletAtPos(const GlobalPosition &globalPos) const {  To determine the density of water for a given state, we build a fluid state with the given conditions: cpp PrimaryVariables values; GetPropType fluidState; fluidState.setTemperature(temperature()); fluidState.setPressure(waterPhaseIdx, /*pressure=*/1e5); fluidState.setPressure(dnaplPhaseIdx, /*pressure=*/1e5);  The density is then calculated by the fluid system: cpp Scalar densityW = FluidSystem::density(fluidState, waterPhaseIdx);  The water phase pressure is the hydrostatic pressure, scaled with a factor: cpp Scalar height = this->fvGridGeometry().bBoxMax()[1] - this->fvGridGeometry().bBoxMin()[1]; Scalar depth = this->fvGridGeometry().bBoxMax()[1] - globalPos[1]; Scalar alpha = 1 + 1.5/height; Scalar width = this->fvGridGeometry().bBoxMax()[0] - this->fvGridGeometry().bBoxMin()[0]; Scalar factor = (width*alpha + (1.0 - alpha)*globalPos[0])/width; values[pressureH2OIdx] = 1e5 - factor*densityW*this->spatialParams().gravity(globalPos)[1]*depth;  The saturation of the DNAPL Trichlorethene is zero on our Dirichlet boundary: cpp values[saturationDNAPLIdx] = 0.0; return values; }  Third, we specify the values for the Neumann boundaries. In our case, we need to specify mass fluxes for our two liquid phases. Inflow is denoted by a negative sign, outflow by a positive sign. cpp NumEqVector neumannAtPos(const GlobalPosition &globalPos) const {  We initialize the fluxes with zero: cpp NumEqVector values(0.0);  At the inlet, we specify an inflow for our DNAPL Trichlorethene. The units are kg/(m^2 s). cpp if (onInlet_(globalPos)) values[contiDNAPLEqIdx] = -0.04; return values; }  Last, we specify the initial conditions. The initial condition need to be set for all primary variables. Here, we take the data from the file that we read in previously. cpp PrimaryVariables initial(const Element& element) const {  The input data is written for a uniform grid with discretization length delta. Accordingly, we need to find the index of our cells, depending on the x and y coordinates, that corresponds to the indices of the input data set. cpp const auto delta = 0.0625; unsigned int cellsX = this->fvGridGeometry().bBoxMax()[0]/delta; const auto globalPos = element.geometry().center(); unsigned int dataIdx = std::trunc(globalPos[1]/delta) * cellsX + std::trunc(globalPos[0]/delta); return initialValues_[dataIdx]; }  We need to specify a constant temperature for our isothermal problem. Fluid properties that depend on temperature will be calculated with this value. cpp Scalar temperature() const { return 293.15; // 10°C }  Additionally, we set a point source. The point source can be solution dependent. It is specified in form of a vector that contains source values for alle phases and positions in space. The first entry is a tupel containing the position in space, the second entry contains a tupel with the source (unit kg/s) for the phases (first phase is the water phase, the second phase is the DNAPL Trichlorethene phase). cpp void addPointSources(std::vector& pointSources) const { pointSources.push_back(PointSource({0.502, 3.02}, {0, 0.1})); }  We define private global functions that are used to determine if a point in space is on the left, right or upper boundary, or at the inlet. cpp private: bool onLeftBoundary_(const GlobalPosition &globalPos) const { return globalPos[0] < this->fvGridGeometry().bBoxMin()[0] + eps_; } bool onRightBoundary_(const GlobalPosition &globalPos) const { return globalPos[0] > this->fvGridGeometry().bBoxMax()[0] - eps_; } bool onUpperBoundary_(const GlobalPosition &globalPos) const { return globalPos[1] > this->fvGridGeometry().bBoxMax()[1] - eps_; } bool onInlet_(const GlobalPosition &globalPos) const { Scalar width = this->fvGridGeometry().bBoxMax()[0] - this->fvGridGeometry().bBoxMin()[0]; Scalar lambda = (this->fvGridGeometry().bBoxMax()[0] - globalPos[0])/width; return onUpperBoundary_(globalPos) && 0.5 < lambda && lambda < 2.0/3.0; }  Our private global variables are the epsilon value and the vector containing the initial values read from file. cpp static constexpr Scalar eps_ = 1e-6; std::vector initialValues_;  This is everything the problem class contains. cpp };  We leave the namespace Dumux here, too. cpp }   Sina Ackermann committed Oct 07, 2019 527 528   Bernd Flemisch committed Oct 07, 2019 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 ## The file main.cc ## The main file This is the main file for the 2pinfiltration example. Here we can see the programme sequence and how the system is solved using newton's method cpp  ### Includes cpp #include  Standard header file for C++, to get time and date information. cpp #include  Standard header file for C++, for in- and output. cpp #include  Dumux is based on DUNE, the Distributed and Unified Numerics Environment, which provides several grid managers and linear solvers. So we need some includes from that. cpp #include #include #include #include #include  In Dumux a property system is used to specify the model. For this, different properties are defined containing type definitions, values and methods. All properties are declared in the file properties.hh. cpp #include  The following file contains the parameter class, which manages the definition of input parameters by a default value, the inputfile or the command line. cpp #include  The file dumuxmessage.hh contains the class defining the start and end message of the simulation. cpp #include #include  we include the linear solver to be used to solve the linear system cpp #include  we include the nonlinear newtons method cpp #include  Further we include assembler, which assembles the linear systems for finite volume schemes (box-scheme, tpfa-approximation, mpfa-approximation). cpp #include  The containing class in the following file defines the different differentiation methods used to compute the derivatives of the residual. cpp #include  we include the spatial discretization methods available in Dumux cpp #include  We need the following class to simplify the writing of dumux simulation data to VTK format. cpp #include  The gridmanager constructs a grid from the information in the input or grid file. There is a specification for the different supported grid managers. cpp #include  we include several files which are needed for the adaptive grid cpp  Sina Ackermann committed Oct 07, 2019 599 600 601 602 603 604 #include #include #include #include #include   Bernd Flemisch committed Oct 07, 2019 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 we include the problem file which defines initial and boundary conditions to describe our example problem cpp #include "problem.hh"  ### Beginning of the main function cpp int main(int argc, char** argv) try { using namespace Dumux;  we define the type tag for this problem cpp using TypeTag = Properties::TTag::PointSourceExample;  We initialize MPI, finalize is done automatically on exit cpp const auto& mpiHelper = Dune::MPIHelper::instance(argc, argv);  We print dumux start message cpp if (mpiHelper.rank() == 0) DumuxMessage::print(/*firstCall=*/true);  We parse command line arguments and input file cpp Parameters::init(argc, argv);  ### Create the grid cpp  A gridmanager tries to create the grid either from a grid file or the input file. cpp GridManager> gridManager; gridManager.init();  ////////////////////////////////////////////////////////// run instationary non-linear problem on this grid ////////////////////////////////////////////////////////// cpp  we compute on the leaf grid view cpp const auto& leafGridView = gridManager.grid().leafGridView();  ### Setup and solving of the problem cpp  #### Setup We create and initialize the finite volume grid geometry, the problem, the linear system, including the jacobian matrix, the residual and the solution vector and the gridvariables. cpp  We need the finite volume geometry to build up the subcontrolvolumes (scv) and subcontrolvolume faces (scvf) for each element of the grid partition. cpp using FVGridGeometry = GetPropType; auto fvGridGeometry = std::make_shared(leafGridView); fvGridGeometry->update();  In the problem, we define the boundary and initial conditions. cpp using Problem = GetPropType; auto problem = std::make_shared(fvGridGeometry);  We call the computePointSourceMap method to compute the point sources. The computePointSourceMap method is inherited from the fvproblem and therefore specified in the dumux/common/fvproblem.hh. It calls the addPointSources method specified in the problem.hh file cpp problem->computePointSourceMap();  we initialize the solution vector cpp using SolutionVector = GetPropType; SolutionVector x(fvGridGeometry->numDofs()); problem->applyInitialSolution(x); auto xOld = x;  and then use the solutionvector to intialize the gridVariables cpp using GridVariables = GetPropType; auto gridVariables = std::make_shared(problem, fvGridGeometry); gridVariables->init(x);  we instantiate the indicator for grid adaption & the data transfer, we read some parameters for indicator from the input file cpp using Scalar = GetPropType; const Scalar refineTol = getParam("Adaptive.RefineTolerance"); const Scalar coarsenTol = getParam("Adaptive.CoarsenTolerance");  We use an indicator for a two-phase flow problem that is saturation-dependent and defined in the file dumux/porousmediumflow/2p/gridadaptindicator.hh. It allows to set the minimum and maximum allowed refinement levels via the input parameters cpp TwoPGridAdaptIndicator indicator(fvGridGeometry);  The data transfer performs the transfer of data on a grid from before to after adaptation and is defined in the file dumux/porousmediumflow/2p/griddatatransfer.hh. Its main functions are to store and reconstruct the primary variables. cpp TwoPGridDataTransfer dataTransfer(problem, fvGridGeometry, gridVariables, x);  we do an initial refinement around sources/BCs. We use the GridAdaptInitializationIndicator defined in dumux/adaptive/initializationindicator.hh for that. cpp GridAdaptInitializationIndicator initIndicator(problem, fvGridGeometry, gridVariables);  we refine up to the maximum level. For every level, the indicator used for the refinement/coarsening is calculated. If any grid cells have to be adapted, the gridvariables and the pointsourcemap are updated. cpp const auto maxLevel = getParam("Adaptive.MaxLevel", 0); for (std::size_t i = 0; i < maxLevel; ++i) {  we calculate the initial indicator for adaption for each grid cell using the initial solution x cpp initIndicator.calculate(x);  we mark the elements that were adapted cpp bool wasAdapted = false; if (markElements(gridManager.grid(), initIndicator)) wasAdapted = adapt(gridManager.grid(), dataTransfer);   Sina Ackermann committed Oct 07, 2019 718 In case of a grid adaptation, the gridvariables and the pointsourcemap are updated.  Bernd Flemisch committed Oct 07, 2019 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 cpp if (wasAdapted) {  We overwrite the old solution with the new (resized & interpolated) one cpp xOld = x;  We initialize the secondary variables to the new (and "new old") solution cpp gridVariables->updateAfterGridAdaption(x);  we update the point source map after adaption cpp problem->computePointSourceMap(); } }  Depending on the initial conditions, another grid adaptation might be necessary. The gridadaptindicator uses the input parameters Adaptive.RefineTolerance and Adaptive.CoarsenTolerance for this step. cpp indicator.calculate(x, refineTol, coarsenTol);  we mark the elements that were adapted cpp bool wasAdapted = false; if (markElements(gridManager.grid(), indicator)) wasAdapted = adapt(gridManager.grid(), dataTransfer);  In case of an additional grid adaptation, the gridvariables and the pointsourcemap are updated again. cpp if (wasAdapted) {  Overwrite the old solution with the new (resized & interpolated) one cpp xOld = x;  Initialize the secondary variables to the new (and "new old") solution cpp gridVariables->updateAfterGridAdaption(x);  Update the point source map cpp problem->computePointSourceMap(); }  we get some time loop parameters from the input file params.input cpp using Scalar = GetPropType; const auto tEnd = getParam("TimeLoop.TEnd"); const auto maxDt = getParam("TimeLoop.MaxTimeStepSize"); auto dt = getParam("TimeLoop.DtInitial");  We initialize the vtkoutput. Each model has a predefined model specific output with relevant parameters for that model. cpp using IOFields = GetPropType; VtkOutputModule vtkWriter(*gridVariables, x, problem->name()); using VelocityOutput = GetPropType; vtkWriter.addVelocityOutput(std::make_shared(*gridVariables)); IOFields::initOutputModule(vtkWriter); // Add model specific output fields vtkWriter.write(0.0);  we instantiate the time loop cpp auto timeLoop = std::make_shared>(0, dt, tEnd); timeLoop->setMaxTimeStepSize(maxDt);  we set the assembler with the time loop because we have an instationary problem cpp using Assembler = FVAssembler; auto assembler = std::make_shared(problem, fvGridGeometry, gridVariables, timeLoop);  we set the linear solver cpp using LinearSolver = AMGBackend; auto linearSolver = std::make_shared(leafGridView, fvGridGeometry->dofMapper());  additionally we set the non-linear solver. cpp using NewtonSolver = Dumux::NewtonSolver; NewtonSolver nonLinearSolver(assembler, linearSolver);  we start the time loop. In each time step before we start calculating a new solution we check if we have to refine the mesh again based on the solution of the previous time step. cpp timeLoop->start(); do {  We only want to refine/coarsen after first time step is finished, not before. The initial refinement was already done before the start of the time loop. This means we only refine when the time is greater than 0. cpp if (timeLoop->time() > 0) {  again we compute the refinement indicator with the TwoPGridAdaptIndicator cpp indicator.calculate(x, refineTol, coarsenTol);  we mark elements and adapt grid if necessary cpp wasAdapted = false; if (markElements(gridManager.grid(), indicator)) wasAdapted = adapt(gridManager.grid(), dataTransfer);  In case of a grid adaptation, the gridvariables and the pointsourcemap are updated again. cpp if (wasAdapted) {  We overwrite the old solution with the new (resized & interpolated) one cpp xOld = x;  We tell the assembler to resize the matrix and set pattern cpp assembler->setJacobianPattern();  We tell the assembler to resize the residual cpp assembler->setResidualSize();  We initialize the secondary variables to the new (and "new old") solution cpp gridVariables->updateAfterGridAdaption(x);  We update the point source map cpp problem->computePointSourceMap(); }  we leaf the refinement step cpp }  Now we start to calculate the new solution of that time step. First we define the old solution as the solution of the previous time step for storage evaluations. cpp assembler->setPreviousSolution(xOld);  We solve the non-linear system with time step control cpp nonLinearSolver.solve(x, *timeLoop);  We make the new solution the old solution cpp xOld = x; gridVariables->advanceTimeStep();  We advance to the time loop to the next step cpp timeLoop->advanceTimeStep();  We write vtk output for each time step cpp vtkWriter.write(timeLoop->time());  We report statistics of this time step cpp timeLoop->reportTimeStep();  We set a new dt as suggested by the newton solver for the next time step cpp timeLoop->setTimeStepSize(nonLinearSolver.suggestTimeStepSize(timeLoop->timeStepSize()));  Sina Ackermann committed Oct 07, 2019 879   Bernd Flemisch committed Oct 07, 2019 880  } while (!timeLoop->finished());  Sina Ackermann committed Oct 07, 2019 881   Bernd Flemisch committed Oct 07, 2019 882  timeLoop->finalize(leafGridView.comm());  Sina Ackermann committed Oct 07, 2019 883   Bernd Flemisch committed Oct 07, 2019 884 885 ### Final Output cpp  Sina Ackermann committed Oct 07, 2019 886   Bernd Flemisch committed Oct 07, 2019 887 888 889 890 891 892 893 print dumux end message cpp if (mpiHelper.rank() == 0) { Parameters::print(); DumuxMessage::print(/*firstCall=*/false); }  Sina Ackermann committed Oct 07, 2019 894   Bernd Flemisch committed Oct 07, 2019 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921  return 0; } // end main catch (Dumux::ParameterException &e) { std::cerr << std::endl << e << " ---> Abort!" << std::endl; return 1; } catch (Dune::DGFException & e) { std::cerr << "DGF exception thrown (" << e << "). Most likely, the DGF file name is wrong " "or the DGF file is corrupted, " "e.g. missing hash at end of file or wrong number (dimensions) of entries." << " ---> Abort!" << std::endl; return 2; } catch (Dune::Exception &e) { std::cerr << "Dune reported error: " << e << " ---> Abort!" << std::endl; return 3; } catch (...) { std::cerr << "Unknown exception thrown! ---> Abort!" << std::endl; return 4; }   Sina Ackermann committed Oct 07, 2019 922   Bernd Flemisch committed Oct 07, 2019 923 ## Results  Sina Ackermann committed Oct 07, 2019 924   Farid Mohammadi committed Oct 07, 2019 925 ![](./img/test_2p_pointsource_adaptive.png)