High order finite volume schemes with IMEX time stepping for the Boltzmann model on unstructured meshes

High order finite difference schemes on non-uniform meshes for the time-fractional Black-Scholes equation

We construct a three-point compact finite difference scheme on a non-uniform mesh for the time-fractional Black-Scholes equation. We show that for special graded meshes used in finance, the Tavella-Randall and the quadratic meshes the numerical solution has a fourth-order accuracy in space. Numerical experiments are discussed. Introduction The Black-Scholes-Merton model for option prices is an ...

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...

Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes

We consider a nonlinear finite volume (FV) scheme for stationary diffusion equation. We prove that the scheme is monotone, i.e. it preserves positivity of analytical solutions on arbitrary triangular meshes for strongly anisotropic and heterogeneous full tensor coefficients. The scheme is extended to regular star-shaped polygonal meshes and isotropic heterogeneous coefficients.

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

Multi-dimensional Optimal Order Detection (MOOD) - A very high-order Finite Volume Scheme for conservation laws on unstructured meshes

TheMulti-dimensional Optimal Order Detection (MOOD) method is an original Very High-Order Finite Volume (FV) method for conservation laws on unstructured meshes. The method is based on an a posteriori degree reduction of local polynomial reconstructions on cells where prescribed stability conditions are not fulfilled. Numerical experiments on advection and Euler equations problems are drawn to ...