Consistent Internal Energy Based Schemes for the Compressible Euler Equations

Numerical schemes for the solution of Euler equations have recently been developed, which involve discretisation internal energy equation, with corrective terms to ensure correct capture shocks, and, more generally, consistency in Lax-Wendroff sense. These may be staggered or colocated, using either structured meshes general simplicial tetrahedral/hexahedral meshes. The time discretization is performed by fractional-step algorithms; these based on semi-implicit pressure correction techniques segregated such a way that only explicit steps are involved (referred hereafter as “explicit” variants). In order positivity density, and pressure, discrete convection operators mass balance carefully designed; they use an upwind technique respect material velocity only. construction fluxes thus does not need any Riemann approximate solver, yields easily implementable algorithms. stability obtained without restriction step scheme under CFL-like condition variants: preservation integral total over computational domain, density energy. first-order satisfies local entropy inequality. If MUSCL-like used limit diffusion, then weaker property holds: inequality satisfied up remainder term shown tend zero space steps, if controlled L∞ BV norms. variant also property, at price estimate could derived from introduction new stabilization momentum balance. Still scheme, above-mentioned same result holds ratio tends zero.