Triangle Based TVD (Total Variation Diminishing) Schemes for Hyperbolic Conversation Laws
INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA
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A triangle based TVD total variation diminishing scheme for the numerical approximation of hyperbolic conservation laws in two space dimensions is constructed. The novelty of the scheme lies in the nature of the preprocessing of the cell averaged data, which is accomplished via a nearest neighbor linear interpolation followed by a slope limiting procedure. Two such limiting procedures are suggested. The resulting method is considerably more simple than other triangle based non-oscillatory approximations which, like this scheme, approximate the flux to second order accuracy. Numerical results for linear advection and Burgers equation are presented. Keywords Hyperbolic conservation laws Limiters Triangular threads.
- Numerical Mathematics