This paper attempts to develop kinetic flux vector splitting (KFVS) for the Euler equations with general pressure laws. It is well known that the gas distribution function for the local equilibrium state plays an important role in the construction of the gas–kinetic schemes. To recover the Euler equations with a general equation of state (EOS), a new local equilibrium distribution is introduced...

Classical and recent numerical schemes for solving hyperbolic conservation laws were analyzed for computational efficiency and application to nonideal gas flows. The Roe-Pike approximate Riemann solver with entropy correction, the Harten second-order scheme and the extension of the Roe-Pike method to secondorder by the MUSCL strategy were compared for one-dimensional flows of an ideal gas. Thes...

Interferometric synthetic aperture radar (InSAR) methods and applications for mapping and monitoring displacements on mountain slopes and subsidence in urban areas were investigated in the EC project MUSCL (Monitoring Urban Subsidence, Cavities and Landslides by means of remote sensing) using various techniques. The area-extended differential InSAR technique was applied for mapping slow slope m...

In this paper we numerically solve the stationary inviscid flow around an airfoil. Using the second-order explicit Runge–Kutta method in combination with the MUSCL scheme and the minmod limiter, we do not obtain a machine accurate solution. This has already been observed in literature and is explained by the non-differentiability of the minmod limiter. An analysis of the limiter shows that it i...

Overland flow and soil erosion play an essential role in water quality and soil degradation. Such processes, involving the interactions between water flow, suspended particles and soil, are classically described by a well-established system of PDE coupling the shallow water equations and the Hairsine-Rose model. The numerical approximation of this coupled system requires advanced methods to pre...

Graphics Processing Unit (GPU) computing is becoming an alternate computing platform for numerical simulations. However, it is not clear which numerical scheme will provide the highest computational efficiency for different types of problems. To this end, numerical accuracies and computational work of several numerical methods are compared using a GPU computing implementation. The Correction Pr...

The goal of this work is to investigate methods for simulating turbulent supersonic flows that include shock waves. Several different types of previously proposed characteristic filters, including total variation diminishing (TVD), monotone upstream-centered scheme for conservation laws (MUSCL), and weighted essentially non-oscillatory (WENO) filters, are investigated in this study. Similar to ...

A new approach for studying wave propagation phenomena in an inviscid gas is presented. This approach can be viewed as the extension of the method of characteristics to the general case of unsteady multidimensional flow. A family of spacetime manifolds is found on which an equivalent one-dimensional (1-D) problem holds. Their geometry depends on the spatial gradients of the flow, and they provi...

We derive fully nonlinear, weakly dispersive model equations for propagation of surface gravity waves in a shallow, homogeneous ocean of variable depth on the surface of a rotating sphere. A numerical model is developed for the weakly nonlinear version of the model based on a combined finite-volume and finitedifference method with a fourth-order MUSCL-TVD scheme in space and a third-order SSP R...