Summation by parts for finite difference approximations for d/dx
Journal of Computational Physics
Fully conservative higher order finite difference schemes for incompressible flow
Journal of Computational Physics
The construction of compatible hydrodynamics algorithms utilizing conservation of total energy
Journal of Computational Physics
High order finite difference schemes on non-uniform meshes with good conversation properties
Journal of Computational Physics
Conservation properties of unstructured staggered mesh schemes
Journal of Computational Physics
Journal of Computational Physics
Symmetry-preserving discretization of turbulent flow
Journal of Computational Physics
Energy and helicity preserving schemes for hydro- and magnetohydro-dynamics flows with symmetry
Journal of Computational Physics
A Volume-of-Fluid based simulation method for wave impact problems
Journal of Computational Physics
Journal of Computational Physics
Higher-order mimetic methods for unstructured meshes
Journal of Computational Physics
Discrete calculus methods for diffusion
Journal of Computational Physics
The numerical simulation of liquid sloshing on board spacecraft
Journal of Computational Physics
Journal of Scientific Computing
Symmetry-preserving upwind discretization of convection on non-uniform grids
Applied Numerical Mathematics
A fully discrete, kinetic energy consistent finite-volume scheme for compressible flows
Journal of Computational Physics
Journal of Computational Physics
Cosymmetry preserving finite-difference methods for convection equations in a porous medium
Applied Numerical Mathematics
Journal of Computational Physics
Statistical relevance of vorticity conservation in the Hamiltonian particle-mesh method
Journal of Computational Physics
Symmetry-preserving discretization of Navier-Stokes equations on collocated unstructured grids
Journal of Computational Physics
A conservative finite difference scheme for Poisson---Nernst---Planck equations
Journal of Computational Electronics
Hi-index | 31.45 |
The paper explains a method by which discretizations of the continuity and momentum equations can be designed, such that they can be combined with an equation of state into a discrete energy equation. The resulting 'MaMEC' discretizations conserve mass, momentum as well as energy, although no explicit conservation law for the total energy is present. Essential ingredients are (i) discrete convection that leaves the discrete energy invariant, and (ii) discrete consistency between the thermodynamic terms. Of particular relevance is the way in which finite volume fluxes are related to nodal values. The method is an extension of existing methods based on skew-symmetry of discrete operators, because it allows arbitrary equations of state and a larger class of grids than earlier methods. The method is first illustrated with a one-dimensional example on a highly stretched staggered grid, in which the MaMEC method calculates qualitatively correct results and a non-skew-symmetric finite volume method becomes unstable. A further example is a two-dimensional shallow water calculation on a rectilinear grid as well as on an unstructured grid. The conservation of mass, momentum and energy is checked, and losses are found negligible up to machine accuracy.