A Simplified TVD Finite Difference Scheme via Artificial Viscosity

Abstract

In this paper we show that the total variation diminishing (TVD) finite difference scheme which was analysed by Sweby [8] can be interpreted as a Lax-Wendroff scheme plus an upwind weighted artificial dissipation term. We then show that if we choose a particular flux limiter and remove the requirement for upwind weighting, we obtain an artificial dissipation term which is based on the theory of TVD schemes, which does not contain any problem dependent parameters and which can be added to existing MacCormack method codes. Finally, we conduct numerical experiments to examine the performance of this new method.

Analysis of numerical methods to solve one-dimensional fluid-dynamic governing equations under impulsive flow in tapered ducts

“…Davis [44] and Yee [45] also worked on these techniques approaching homentropic flow. In these flow conditions, the Davis flux limiter technique (DTVD) can be obtained just by adding a viscous term to the second step of Richtmyer and Morton scheme.…”

WhiskyMHD: a new numerical code for general relativistic magnetohydrodynamics

“…In [3,4], for instance, the effects of a Kerr black hole on magnetohydrodynamical accretion have been studied, with particular attention being paid to the transfer of energy and angular momentum. Koide et al [5], on the other hand, have developed a numerical code based on the artificial-viscosity approach proposed by Davis [6] to perform the first simulations of jet formation in general relativity [7] and to study the possibility of extracting the rotational energy from a Kerr black hole [8,9]. Furthermore, a distinct numerical code has been constructed by De Villiers and Hawley [10] using the formulation proposed in [11,12] to carry out a series of studies on accretion flows around Kerr black holes [13][14][15].…”

Superheated fuel injection modeling: An engineering approach

“…This method is second order accurate in both space and time. A TVD (Total Variation Diminishing) scheme as proposed by Davis is used as flux limiter [18,19].…”