An adaptive mesh strategy for high compressible flows based on nodal re-allocation

An adaptive mesh strategy based on nodal re-allocation is presented in this work. This technique is applied to problems involving compressible flows with strong shocks waves, improving the accuracy and efficiency of the numerical solution. The initial mesh is continuously adapted during the solution process keeping, as much as possible, mesh smoothness and local orthogonality using an unconstrained nonlinear optimization method. The adaptive procedure, which is coupled to an edge-based error estimate aiming to equidistribute the error over the cell edges is the main contribution of this work. The flow is simulated using the Finite Element Method (FEM) with an explicit one-step Taylor- Galerkin scheme, in which an Arbitrary Lagrangean-Eulerian (ALE) description is employed to take into account mesh movement. Finally, to demonstrate the capabilities of the adaptive process, several examples of compressible inviscid flows are presented