We consider the convergence and stability property of MUSCL relaxing schemes applied to conservation laws with stiff source terms. The maximum principle for the numerical schemes will be established. It will be also shown that the MUSCL relaxing schemes are uniformly l and TV-stable in the sense that they are bounded by a constant independent of the relaxation parameter =, the Lipschitz constan...

We consider the convergence and stability property of MUSCL relaxing schemes applied to conservation laws with stii source terms. The maximum principle for the numerical schemes will be established. It will be also shown that the MUSCL relaxing schemes are uniformly l 1-and T V-stable in the sense that they are bounded by a constant independent of the relaxation parameter , the Lipschitz consta...

We present a general L stability result for a generic finite volume method for hyperbolic scalar equations coupled with a large class of reconstruction. We show that the stability is obtained if the reconstruction respects two fundamental properties: the convexity property and the sign inversion property. We also introduce a new MUSCL technique, the multislope MUSCL technique, based on the appr...

Computational Fluid Dynamics (CFD) is used as a common design tool in the aerospace industry. UPACS, a package for CFD, is convenient for users, since a customized simulator can be built just by selecting desired functions. The problem is its computation speed, which is difficult to enhance by using the clusters due to its complex memory access patterns. As an economical solution, accelerators ...

We analyze the energy stability of the standard MUSCL scheme. The analysis is possible by reformulating the MUSCL scheme in the framework of summation-by-parts (SBP) operators including an artificial dissipation. The effect of different slope limiters is studied. It is found that all the slope limiters do not lead to the correct sign of the entries in the dissipation matrix. The implication of ...

The goal of this study is to apply the MUSCL scheme to the linear advection equation on general unstructured grids and to examine the eigenvalue stability of the resulting linear semi-discrete equation. Although this semi-discrete scheme is in general stable on cartesian grids, numerical calculations of spectra show that this can sometimes fail for generalizations of the MUSCL method to unstruc...

The accurate prediction of helicopter rotor blade–vortex interaction (BVI) noise is challenging. This paper presents an implementation the seventh-order improved weighted essentially non-oscillatory (WENO-Z) scheme for predicting BVI using a high-resolution numerical method based on Reynolds-averaged Navier–Stokes and Ffowcs Williams–Hawkings equations. WENO-Z utilized to minimize inherent diss...

We propose to extend the well-known MUSCL-Hancock scheme for Euler equations to the induction equation modeling the magnetic field evolution in kinematic dynamo problems. The scheme is based on an integral form of the underlying conservation law which, in our formulation, results in a “finite-surface” scheme for the induction equation. This naturally leads to the well-known “constrained transpo...

For the high order numerical approximation of hyperbolic systems of conservation laws, we propose to use as a building principle an entropy diminishing criterion instead of the familiar total variation diminishing criterion introduced by Harten for scalar equations. Based on this new criterion, we derive entropy diminishing projections that ensure, both, the second order of accuracy and all of ...

Multidimensional Positive Definite Advection Transport Algorithm (MPDATA) and Monotonic Upstream Schemes for Conservation Laws (MUSCL) are compared and evaluated in a biogeochemical-like tracer model. Based on the MUSCL scheme, an adapted scheme for r-coordinate models (MUSCL_VD) is presented. These schemes are first implemented in idealized experiments configured for a closed channel with and ...