Alexander Kurganov
Southern University of Science and Technology
Title
Central-Upwind Schemes with Reduced Numerical Dissipation
Abstract
Central-upwind schemes are Riemann-problem-solver-free Godunov-type finite-volume schemes, which are, in fact, non-oscillatory central schemes with a certain upwind flavor: derivation of the central-upwind numerical fluxes is based on the one-sided local speeds of propagation, which can be estimated using the largest and smallest eigenvalues of the Jacobian.
I will introduce two new classes of central-upwind schemes with reduced numerical dissipation. First, we will use a sub-cell resolution at the projection step to enhance the resolution of contact waves, which are typically badly affected by excessive numerical dissipation present in numerical methods. The second approach is based on the utilization of the local characteristic decomposition for the modification of the numerical diffusion of the central-upwind schemes. Both approaches help to significantly reduce the amount of numerical dissipation present in central-upwind schemes without risking large spurious oscillation. Applications to several hyperbolic systems of conservation laws will be discussed.