Volume conservation method for the three-dimensional front-tracking method

A Conservative Front Tracking Method for Hyperbolic Conservation Laws

Three-Dimensional Front Tracking

We describe a three dimensional front tracking algorithm, discuss its numerical implementation, and present studies to validate the correctness of this approach. Based on the results of the two dimensional computations, we expect three dimensional front tracking to improve signiicantly computational eeciencies for problems dominated by discontinu-ities. In some cases, for which the interface co...

On the Accuracy of a Numerical Method for Two-dimensional Scalar Conservation Laws Based on Dimensional Splitting and Front Tracking

A rigorous proof of an error estimate for a numerical method for two-dimensional scalar conservation laws is presented. The numerical method under consideration is based on the use of dimensional splitting and front tracking to solve the one-dimensional equations. It is shown that the error is bounded by C(((t) 1=2 + ((x) 1=2 +), where x is the space step, t is the time step, is the parameter m...

Spectral (finite) volume method for conservation laws on unstructured grids V: Extension to three-dimensional systems

In this paper, the fourth in a series, the spectral volume (SV) method is extended to multi-dimensional systems – the 2D Euler equations. The focus of this paper is to study the performance of the SV method on multidimensional nonlinear systems, and to verify that high order solution accuracy up to fourth-order can be achieved for the systems of conservation laws. Implementation details includi...

A Three-Dimensional, Unsplit Godunov Method for Scalar Conservation Laws

Linear advection of a scalar quantity by a specified velocity field arises in a number of different applications. Of particular interest here is the transport of species and energy in low Mach number models for combustion, atmospheric flows, and astrophysics, as well as contaminant transport in Darcy models of saturated subsurface flow. An important characteristic of these problems is that the ...