Lagrange-Flux Schemes: Reformulating Second-Order Accurate Lagrange-Remap Schemes for Better Node-Based HPC Performance

Lagrange-flux Eulerian Schemes for Compressible Multimaterial Flows

This paper is devoted to the redesign of the Lagrangian remapping process for compressible Hydrodynamics in order to achieve better computational performance. As an unintended outcome, the analysis has lead us to the discovery of a new family of solvers – the so-called Lagrange-flux schemes – that appear to be very promising for the CFD community. Results obtained with the Lagrange-flux approac...

On the relationship between Semi-Lagrangian and Lagrange-Galerkin schemes

On simplifying 'incremental remap'-based transport schemes

The flux-form incremental remapping transport scheme introduced by Dukowicz and Baumgardner [1] converts the transport problem into a remapping problem. This involves identifying overlap areas between quadrilateral flux-areas and regular square grid cells which is non-trivial and leads to some algorithm complexity. In the simpler swept area approach (originally introduced by Hirt et al. [2]) th...

High-Order Flux Reconstruction Schemes

There is an increasing desire among industrial practitioners of computational fluid dynamics to undertake high-fidelity scale-resolving simulations of unsteady flows within the vicinity of complex geometries. Such simulations require numerical methods that can operate on unstructured meshes with low numerical dissipation. The flux reconstruction (FR) approach describes one such family of numeri...

Some considerations for high-order ‘incremental remap’-based transport schemes: edges, reconstructions, and area integration

The problem of two-dimensional tracer advection on the sphere is extremely important in modeling of geophysical fluids and has been tackled using a variety of approaches. A class of popular approaches for tracer advection include ‘incremental remap’ or cell-integrated semi-Lagrangian-type schemes. These schemes achieve high-order accuracy without the need for multistage integration in time, are...