A High Order Accurate Difference Scheme for Complex Flow Fields

A Fourth Order Accurate Finite Difference Scheme for the Elastic Wave Equation in Second Order Formulation

We present a fourth order accurate finite difference method for the elastic wave equation in second order formulation, where the fourth order accuracy holds in both space and time. The key ingredient of the method is a boundary modified fourth order accurate discretization of the second derivative with variable coefficient, (μ(x)ux)x. This discretization satisfies a summation by parts identity ...

A High-order Compact Finite-difference Scheme for Large-eddy Simulation of Active Flow Control

High-order Accurate Spectral Difference Method for Shallow Water Equations

ABSTRACT The conservative high-order accurate spectral difference method is presented for simulation of rotating shallowwater equations. The method is formulated using Lagrange interpolations on Gauss-Lobatto points for the desired order of accuracy without suffering numerical dissipation and dispersion errors. The optimal third-order total variation diminishing (TVD) Runge-Kutta algorithm is u...

High-order accurate difference schemes for the Hodgkin-Huxley equations

A novel approach for simulating potential propagation in neuronal branches with high accuracy is developed. The method relies on high-order accurate difference schemes using the Summation-By-Parts operators with weak boundary and interface conditions applied to the Hodgkin-Huxley equations. This work is the first demonstrating high accuracy for that equation. Several boundary conditions are con...

High-Order Accurate Methods for High-Speed Flow

This work focuses on high-order numerical schemes for conservation laws with emphasis on problems that admit discontinuous solutions. We will investigate several enabling techniques with the aim to construct robust methods for unstructured meshes capable of reliably producing globally high-order accurate results even in the presence of discontinuities. We use spectral and pseudo-spectral scheme...