We present a novel implicit scheme for the numerical solution of time-dependent conservation laws. The core idea presented method is to exploit and approximate mixed spatial-temporal derivative that occurs naturally when deriving some second order accurate schemes in time. Such an approach introduced context Lax-Wendroff (or Cauchy-Kowalevski) procedure time not completely replaced by space der...

The Landau-Lifshitz Navier-Stokes (LLNS) equations incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. This paper examines explicit Eulerian discretizations of the full LLNS equations. Several computational fluid dynamics approaches are considered (including MacCormack's two-step Lax-Wendroff scheme and the piecewise parabolic method) and are found to giv...

Computer simulation of the thermodynamics and dynamics of an intercooled two-stage two-cylinder reciprocating air compressor system is reported and the obtained results discussed. The main emphasis is placed upon modeling the pressure-wave motion in the interconnecting pipework for which the governing equations were solved by means of two different methods: the characteristic mesh method and th...

We propose an investigation of the residual distribution schemes for the numerical approximation of two dimensional hyperbolic systems of conservation laws on general quadrilateral meshes. In comparison to the use of triangular cells, usual basic features are recovered, an extension of the Upwinding concept is given, and a Lax-Wendroff like theorem is adapted for consistency. We show how to ret...

We introduce two kinds of explicit solutions to the convection-reaction equation, ut + (|u| /q)x = u, u, x ∈ R, t ∈ R , q > 1, and employ them to test properties of various computational schemes. From this test we observe that computed solutions using Lax-Friedrichs, MacCormack and Lax-Wendroff schemes break down in a finite time. On the other hand some other schemes including WENO, NT and Godu...

We prove in this paper the Lax–Wendroff consistency of a general finite volume convection operator acting on discrete functions which are possibly not piecewise-constant over cells mesh and time steps. It yields an extension theorem for colocated or non-colocated schemes. This result is obtained polygonal polyhedral meshes, under assumptions which, usual practical cases, essentially boil down t...

In this paper, we study the stability of a numerical boundary treatment high order compact finite difference methods for parabolic equations. The schemes could achieve very accuracy with relatively small stencils. To match convergence in interior domain, take simplified inverse Lax–Wendroff (SILW) procedure (Tan et al., 2012; Li 2017) as our treatment. third total variation diminishing (TVD) Ru...