Shock-Capturing Schemes with Entropy Corrections and Dynamically Adaptive Unstructured Meshes

A dynamical grid-adaptation method coupled with the numerical scheme on unstructured meshes is described. The discontinuity capturing properties of such methods ensure a high precision for the global solution. Entropy corrections for centered space approximation numerical schemes which do not preserve entropy are discussed. In particular, the problem of spurious entropy production by the numerics near solid wall boundaries which present discontinuous contours can be overcome by a localised use of an entropy-preserving Riemann solver.