We develop and analyze an improved version of the Multi-Stage (MUSTA) approach to the construction of upwind Godunov-type fluxes whereby the solution of the Riemann problem, approximate or exact, is not required. The new MUSTA schemes improve upon the original schemes in terms of monotonicity properties, accuracy and stability in multiple space dimensions. We incorporate the MUSTA technology in...

The issue of boundedness in the discretisation of the convection term of transport equations has been widely discussed. A large number of local adjustment practices has been proposed, including the well-known TVD and NVD families of diierencing schemes. All of those use some sort of an \unboundedness indicator" in order to determine the parts of the domain where intervention in the discretisati...

Based on the developed thirdand fourth-order upwind compact finite difference(FD) schemes, a new high-order weighted upwind FD approach, which is called combined compact upwind FD method, is proposed for decreasing dispersive(phase) and dissipative errors of the finite difference approximations. The newly proposed combined compact upwind FD schemes have the characters of group velocity control ...

In this paper, we develop a second-order well-balanced central-upwind scheme for the Euler equations of gas dynamics with gravitation. The proposed scheme is capable of exactly preserving steady-state solutions expressed in terms of a nonlocal equilibrium variable. A crucial step in the construction of the second-order scheme is a well-balanced piecewise linear reconstruction of equilibrium var...

In this paper, we present a novel hybrid nonlinear explicit-compact scheme for shock-capturing based on boundary variation diminishing (BVD) reconstruction. our approach, combine non-dissipative sixth-order central compact interpolation and fifth-order monotonicity preserving (MP5) through the BVD algorithm. For smooth solution, reconstruction chooses highest order possible interpolation, which...

We show that there are simple one dimensional problems for which the MHD code, ZEUS, generates significant errors, whereas upwind conservative schemes perform very well on these problems.

Article history: Received 10 January 2008 Received in revised form 16 June 2008 Accepted 11 August 2008 Available online 23 August 2008

This paper is concerned with computing viscosity solutions of Hamilton–Jacobi equations using high-order Godunov-type projection-evolution methods. These schemes employ piecewise polynomial reconstructions, and it is a well-known fact that the use of more compressive limiters or higher-order polynomial pieces at the reconstruction step typically provides sharper resolution. We have observed, ho...

We introduce a central-upwind scheme for oneand two-dimensional systems of shallow-water equations with horizontal temperature gradients (the Ripa system). The scheme iswell-balanced, positivity preserving and does not develop spurious pressure oscillations in the neighborhood of temperature jumps, that is, near the contact waves. Such oscillations would typically appear when a conventional God...