Algebraic limitations on two-dimensional hydrodynamics simulations
Algebraic limitations imposed by the use of connected straightline segments to define meshes for hydrodynamics simulations in two-dimensional cylindrical geometries are shown. It is shown that in the simplest smooth isentropic flow of the spherical expansion of a gas with point symmetry, commonly, and currently, used finite difference, finite volume, or finite element staggered grid hydrodynamics equations cannot simultaneously preserve energy, entropy and sphericity on an equal-angle mesh. Exact difference representations of interface (cell face) pressures and work terms and of the elements of the strain rate tensor in a cell are shown.
scientific article; zbMATH DE number 881871