several ways and sets of compatible formulas for staggered grid hydrodynamics [1][2][3] which are derived to inherently conserve Algebraic limitations imposed by the use of connected straightline segments to define meshes for hydrodynamics simulations in two-total energy are displayed. Compatible formulas have the propdimensional cylindrical geometries are shown. It is shown that in erty that different arrangements of pressure, mass, area, and the simplest smooth isentropic flow of the spherical expansion of velocity terms in the total energy conservation equation reprea gas with point symmetry, commonly, and currently, used finite sent the momentum equation at cell vertices, the internal and difference, finite volume, or finite element staggered grid hydrodytotal energy equations in the cell, and the interface work done namics equations cannot simultaneously preserve energy, entropy, and sphericity on an equal-angle R Οͺ β° mesh. It is further shown by (or on) the faces of the cells. The interface pressure on why finite difference codes tend to preserve sphericity and entropy, the cell faces is a compatible derived quantity. Any particular while finite element codes tend to preserve sphericity and energy. equation can be used as a starting point and the others follow.
Exact difference representations of interface (cell face) pressures
But even with these formulas, algebraic limitations in cylindriand work terms and of the elements of the strain rate tensor in a cal geometry do not allow the simultaneous conservation of cell are shown.