Mesh optimization to improve the stability of finite-volume methods on unstructured meshes

The new approach proposed here improves the stability of unstructured mesh finite-volume CFD calculations by moving vertices in the mesh as an a posteriori process. In this process, we exploit the gradients of eigenvalues with respect to the local changes in the mesh to find directions and magnitudes of mesh perturbations that will make the Jacobian of a semi-discrete system of equations negative semi-definite. This will ensure the energy stability of the system, consequently resulting in convergence. Our numerical results have shown that the proposed method was able to locate the problematic parts of the mesh as well as reconstruction responsible for instabilities for several physical problems.