A Sharp Interface and Fully Conservative Scheme for Computing Nonclassical Shocks


We present a sharp interface and fully conservative numerical strategy for computing nonclassical solutions of scalar conservation laws. The difficult point is to impose at the discrete level a prescribed kinetic relation along each nonclassical discontinuity. Our method is based on a relevant reconstruction technique operating on each cell which is expected to contain a nonclassical shock. To prove the validity of our approach, we state some important stability properties and numerical tests are proposed. The convergence is also illustrated numerically.

Numerical Mathematics and Advanced Applications