diff --git a/doc/doxygen/dumux.bib b/doc/doxygen/dumux.bib index ad5f39df176dba77f587472ee2ab69dfb8471530..770bee3928a0655b0a9a39a6b080d95f9f7263d7 100644 --- a/doc/doxygen/dumux.bib +++ b/doc/doxygen/dumux.bib @@ -2076,3 +2076,28 @@ author = {F. Fichot and F. Duval and N. Trégourès and C. Béchaud and M. Quint issn = {0022-3654}, doi = {10.1021/j150514a018} } + +@Article{Schneider2024, + title = {Stable and locally mass- and momentum-conservative control-volume finite-element schemes for the {Stokes} problem}, + volume = {420}, + ISSN = {0045-7825}, + DOI = {10.1016/j.cma.2023.116723}, + journal = {Computer Methods in Applied Mechanics and Engineering}, + publisher = {Elsevier BV}, + author = {Schneider, Martin and Koch, Timo}, + year = {2024}, + month = feb, + pages = {116723} +} + +@article{Harlow1965, + doi = {10.1063/1.1761178}, + year = {1965}, + publisher = {{AIP} Publishing}, + volume = {8}, + number = {12}, + pages = {2182}, + author = {Francis H. Harlow and J. Eddie Welch}, + title = {Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface}, + journal = {Physics of Fluids} +} diff --git a/doc/doxygen/groups/details/fcdiamond.md b/doc/doxygen/groups/details/fcdiamond.md new file mode 100644 index 0000000000000000000000000000000000000000..0c03b2f999862edc1835772882b829470e143759 --- /dev/null +++ b/doc/doxygen/groups/details/fcdiamond.md @@ -0,0 +1,13 @@ +@addtogroup DiamondDiscretization + +The diamond method is a control-volume finite element scheme with piecewise linear discontinuous basis functions +(Crouzeix-Raviart on simplices and Rannacher-Turek on quadrilaterals). The basis functions are continuous only at +the element face centers but are generally discontinuous along the facet and thus also at vertices. +Control volumes are constructed around the face centers of the element faces of the primary grid. +This results in diamond-shaped control volumes that form a dual grid. + +{html: width=50%} + +The diamond CVFE scheme can, for example, be used for the velocity combined with cell-centered FV schemes for the pressure +to discretize the incompressible Stokes equation (in formulation with full velocity gradient in the flux term; for the formulation +with symmetric velocity gradient additional face stabilization terms are required) on unstructured grids. diff --git a/doc/doxygen/groups/details/fcstaggered.md b/doc/doxygen/groups/details/fcstaggered.md new file mode 100644 index 0000000000000000000000000000000000000000..1311bef70b2f43fe68c962e5e5420fe8e874478c --- /dev/null +++ b/doc/doxygen/groups/details/fcstaggered.md @@ -0,0 +1,12 @@ +@addtogroup FaceCenteredStaggeredDiscretization + +The finite volume method on a staggered grid is a classical discretization scheme for the momentum balance of the Navier-Stokes equations \cite Harlow1965. +It is constructed on Cartesian (tensor product) grids. Here, we use the same abstraction as for other finite volume and CVFE schemes and split +the staggered (shifted) control volumes into element-wise parts: sub control volumes. Fluxes are assembled over sub control volumes faces, +where two control volume faces are fully contained in an element (these are called frontal faces), and two faces are shared between +neighboring elements and therefore split into two sub control volume faces (these are called lateral faces). + +{html: width=50%} + +The image shows the control volume partition in 2D. +It also shows the neighboring degrees of freedom involved in the interpolation of gradients at the flux integration points. diff --git a/doc/doxygen/groups/details/pq1bubble.md b/doc/doxygen/groups/details/pq1bubble.md new file mode 100644 index 0000000000000000000000000000000000000000..cd23cea3190696f496072e7d611abb4c6f9f416f --- /dev/null +++ b/doc/doxygen/groups/details/pq1bubble.md @@ -0,0 +1,11 @@ +@addtogroup PQ1BubbleDiscretization + +An extension of the box method is obtained when enriching the trial space by a bubble function. +While the box method is a control-volume finite element scheme with piecewise constant basis functions, +the bubble scheme uses basis functions enriched by a bubble function. The scheme is introduced in @cite Schneider2024. + +{html: width=50%} + +The additional degree of freedom at the element center is used to ensure stability, for example in the case +of velocity spaces for the Stokes problem. An additional overlapping control volume is introduced for +the element degree of freedom. \ No newline at end of file