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style="font-style:normal;font-weight:normal;font-size:12.6288147px;line-height:125%;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#008080;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" + x="224.86328" + y="491.94003" + id="text4391" + sodipodi:linespacing="125%"><tspan + sodipodi:role="line" + id="tspan4393" + x="224.86328" + y="491.94003">2</tspan></text> + <text + xml:space="preserve" + style="font-style:normal;font-weight:normal;font-size:12.6288147px;line-height:125%;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" + x="186.83478" + y="471.49045" + id="text4395" + sodipodi:linespacing="125%"><tspan + sodipodi:role="line" + id="tspan4397" + x="186.83478" + y="471.49045">0</tspan></text> + <text + xml:space="preserve" + style="font-style:normal;font-weight:normal;font-size:12.6288147px;line-height:125%;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#008080;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" + x="222.55444" + y="434.31277" + id="text4403" + sodipodi:linespacing="125%"><tspan + sodipodi:role="line" + id="tspan4405" + x="222.55444" + y="434.31277">3</tspan></text> + <text + xml:space="preserve" + style="font-style:normal;font-weight:normal;font-size:12.6288147px;line-height:125%;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#008080;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" + x="433.65903" + y="475.3475" + id="text4407" + sodipodi:linespacing="125%"><tspan + sodipodi:role="line" + id="tspan4409" + x="433.65903" + y="475.3475">localNormalFaceIdx</tspan></text> + <text + xml:space="preserve" + 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x="247.02138" + y="453.44824">1</tspan></text> + </g> +</svg> diff --git a/dumux/discretization/staggered/freeflow/staggeredgeometryhelper.hh b/dumux/discretization/staggered/freeflow/staggeredgeometryhelper.hh index d78655e90582b2d31e6807dbecec6a39e1ac96e4..7cc7086edc7ea8627ceb6a2e1a47eaf144838f84 100644 --- a/dumux/discretization/staggered/freeflow/staggeredgeometryhelper.hh +++ b/dumux/discretization/staggered/freeflow/staggeredgeometryhelper.hh @@ -66,6 +66,11 @@ inline static unsigned int directionIndex(Vector&& vector) * \ingroup StaggeredDiscretization * \brief Helper class constructing the dual grid finite volume geometries * for the free flow staggered discretization method. + * + * A visualization of the variables that are in this document can be found in the following image: + * + * \image html staggeredgeometry.png + * */ template<class GridView> class FreeFlowStaggeredGeometryHelper diff --git a/dumux/multidomain/subdomainstaggeredlocalassembler.hh b/dumux/multidomain/subdomainstaggeredlocalassembler.hh index af978a29ac258164df0bb745347667cc2c52e943..ca6b17dacd2bdbb1dfc26c2fe10b39f9991b8107 100644 --- a/dumux/multidomain/subdomainstaggeredlocalassembler.hh +++ b/dumux/multidomain/subdomainstaggeredlocalassembler.hh @@ -467,6 +467,20 @@ class SubDomainStaggeredLocalAssembler; * \ingroup StaggeredDiscretization * \ingroup MultiDomain * \brief Staggered scheme local assembler using numeric differentiation and implicit time discretization + * + * The assembly of the cellCenterResidual is done element-wise, the assembly of the face residual is done half-element-wise. + * + * A sketch of what this means can be found in the following image: + * + * \image html staggered_halfelementwise.png + * + * Half-element wise assembly means, that integrals are +split into contributions from the left and right part of the staggered control volume. For an example term \f$\int_{\Omega}\varrho u\text{d}\Omega\f$ this reads +\f$\int_{\Omega}\varrho u\text{d}\Omega = \frac{1}{2}\Omega_\text{left}\varrho_\text{left}u+\frac{1}{2}\Omega_\text{right}\varrho_\text{right}u\f$. + +During assembly, \f$\frac{1}{2}\Omega_\text{left}\varrho_\text{left}u\f$ is added to the residual of the +staggered control volume \f$\Omega\f$, when the loops reach the scvf within element \f$\Omega_\text{left}\f$. \f$\frac{1}{2}\Omega_\text{right}\varrho_\text{right}u\f$ is added to the residual of \f$\Omega\f$, when the loops reach the scvf within in element \f$\Omega_\text{right}\f$. +Other terms are split analogously. */ template<std::size_t id, class TypeTag, class Assembler> class SubDomainStaggeredLocalAssembler<id, TypeTag, Assembler, DiffMethod::numeric, /*implicit=*/true>