The Godunov method for conservation laws produces numerical solutions that are total-variation diminishing (TVD) and converge to weak solutions which satisfy the entropy condition (Entropy Consistency), but the method is only first order accurate. Many second and higher order accurate Godunov–type methods have been developed by various researchers. Although these high order methods perform very...

In the present paper a multigrid technique for three-dimensional perfect gas hypersonic vis-cous ows has been developed, employing a Total Variation Diminishing (TVD) discretization and an upwind correction prolongation, based on a monotonic reconstruction of coarse-grid correction. The methodology has good convergence properties, both for boundary layer ows and complex shock wave-boundary laye...

In this note we consider the analysis of the wave-front shape resulting from the sudden release of a finite volume of water over an inclined plane bed of arbitrary bottom slope. To that end we use the one-dimensional turbulent shallow water equations with a constant friction factor. We propose an asymptotic analytical solution for the height and velocity in the wave tip region based on the velo...

ABSTRACT We introduce a new troubled-cell indicator for the discontinuous Galerkin (DG) methods for solving hyperbolic conservation laws. This indicator can be defined on unstructured meshes for high order DG methods and depends only on data from the target cell and its immediate neighbors. It is able to identify shocks without PDE sensitive parameters to tune. Extensive oneand two-dimensional ...

The main goal of this paper is to analyze the exergy losses during the shock and rarefaction wave of hydrogen-air mixture. First, detonation parameters pressure, temperature, density, and species mass fraction are calculated for three cases where the hydrogen mass fraction in air is 1.5%, 2.5%, and 5%. Then, exergy efficiency is used as objective criteria of performance evaluation. A two-dimens...

In this paper we present the MmB schemes, which preserve the local maximum and minimum bounds of the initial data in the smallest union of mesh elements of previous time step containing the domain of dependence of the solution on the mesh element with center at point P under consideration. In 1-D, the MmB schemes are almost identical with TVD schemes. As well-known, there is no second-order TVD...

The efficiency of high order accurate schemes for the solution of unsteady hyperbolic conservation laws is adversely affected by time-step restrictions that arise from monotonicity requirements. When applied to the solution of problems involving discontinuities, these restrictions render conventional high order implicit time integration schemes impractical. In the present study, a new single st...

This work addresses a theory of convergence for finite volume methods applied to linear equations. A non-consistent model problem posed in an abstract Banach space is proved to be convergent. Then various examples show that the functional framework is non-empty. Convergence with a rate h 1 2 of all TVD schemes for linear advection in 1D is an application of the general result. Using duality tec...

The present derivation of split-flux formulas has the following features:(l) it includes several particular formuFlux-vector and flux-difference splittings for the inlas derived elsewhere for ideal gases, (2) it avoids unnecesviscid terms of the compressible flow equations are derived sary assumptions or approximations, (3) it avoids unnecunder the assumption of a general equation of state for ...

A two-dimensional mountainous mass flow dynamic procedure solver (Massflow-2D) using the MacCormack-TVD finite difference scheme is proposed. The solver is implemented in Matlab on structured meshes with variable computational domain. To verify the model, a variety of numerical test scenarios, namely, the classical one-dimensional and two-dimensional dam break, the landslide in Hong Kong in 199...