The University of Reading Department

A cell by cell anisotropic adaptive mesh technique is combined with a staggered mesh Lagrange plus remap finite element ALE code for the solution of the Euler equations. The quadrilateral finite elements may be subdivided isotropically or anisotropically in a cell by cell manner. An efficient computational method is proposed, which only solves on the finest level of resolution that exists for each part of the domain, referred to as the Dynamic Mesh, with disjoint or hanging nodes being used at resolution transitions. The Lagrangian, equipotential mesh relaxation and advection (solution remapping) steps are generalised so that they may be applied on the unstructured Dynamic Mesh. The method is validated on a series of test problems and it is shown that the anisotropic adaptive mesh method can give a dramatic decrease in run time (run times are up to nine times faster on the test problems used).