A direct Arbitrary-Lagrangian–Eulerian ADER-WENO finite volume scheme on unstructured tetrahedral meshes for conservative and non-conservative hyperbolic systems in 3D

Optimising UCNS3D, a High-Order finite-Volume WENO Scheme Code for arbitrary unstructured Meshes

UCNS3D is a computational-fluid-dynamics (CFD) code for the simulation of viscous flows on arbitrary unstructured meshes. It employs very high-order numerical schemes which inherently are easier to scale than lower-order numerical schemes due to the higher ratio of computation versus communication. In this white paper, we report on optimisations of the UCNS3D code implemented in the course of t...

FORCE schemes on unstructured meshes I: Conservative hyperbolic systems

In this paper we propose a new high order accurate centered path-conservative method on unstructured triangular and tetrahedral meshes for the solution of multidimensional non-conservative hyperbolic systems, as they typically arise in the context of compressible multi-phase flows. Our path-conservative centered scheme is an extension of the centered method recently proposed in [36] for conserv...

Entropy Conservative and Entropy Stable Finite Volume Schemes for Multi-dimensional Conservation Laws on Unstructured Meshes

Third Order WENO Scheme on Three Dimensional Tetrahedral Meshes

We extend the weighted essentially non-oscillatory (WENO) schemes on two dimensional triangular meshes developed in [7] to three dimensions, and construct a third order finite volume WENO scheme on three dimensional tetrahedral meshes. We use the Lax-Friedrichs monotone flux as building blocks, third order reconstructions made from combinations of linear polynomials which are constructed on div...

Efficient conservative ADER schemes based on WENO reconstruction and space-time predictor in primitive variables

We present a new version of conservative ADER-WENO finite volume schemes, in which both the high order spatial reconstruction as well as the time evolution of the reconstruction polynomials in the local space-time predictor stage are performed in primitive variables, rather than in conserved ones. To obtain a conservative method, the underlying finite volume scheme is still written in terms of ...