A direct Eulerian generalized Riemann problem (GRP) scheme is derived for compressible fluid flows. Riemann invariants are introduced as the main ingredient to resolve the generalized Riemann problem (GRP) directly for the Eulerian formulation. The crucial auxiliary Lagrangian scheme in the original GRP scheme is not necessary in the present framework. The delicate sonic cases can be easily tre...

We investigate the scale–dependence of Eulerian volume averages of scalar functions on Riemannian three–manifolds. We propose a complementary view of a Lagrangian scaling of variables as opposed to their Eulerian averaging on spatial domains. This program explains rigorously the origin of the Ricci deformation flow for the metric, a flow which, on heuristic grounds, has been already suggested a...

In this work, we introduce a new method for generating Lagrangian computational meshes from Eulerian-based data. We focus specifically on shock physics problems that are relevant to Eulerian-based codes that generate volume fraction data on a Cartesian grid. A step-by-step procedure for generating an allhexahedral mesh is presented. We focus specifically on the challenges of developing a parall...