A Front Tracking Method Based on Runge-Kutta Discontinuous Galerkin Methods

A Runge-Kutta discontinuous Galerkin method for viscous flow equations

This paper presents a Runge–Kutta discontinuous Galerkin (RKDG) method for viscous flow computation. The construction of the RKDG method is based on a gas-kinetic formulation, which not only couples the convective and dissipative terms together, but also includes both discontinuous and continuous representation in the flux evaluation at a cell interface through a simple hybrid gas distribution ...

A Runge – Kutta discontinuous Galerkin conservative level set method

We present a Runge-Kutta discontinous Galerkin (RKDG) method to solve the level set advection equation arising in the conservative level set method. We show results obtained using the method of manufactured solutions demonstrating k + 1 order accuracy for k-th order Legendre polynomial basis functions. The RKDG conservative level set method yields superior results compared to standard finite di...

Runge - Kutta Discontinuous Galerkin Method for the Boltzmann Equation

In this thesis we investigate the ability of the Runge-Kutta Discontinuous Galerkin (RKDG) method to provide accurate and efficient solutions of the Boltzmann equation. Solutions of the Boltzmann equation are desirable in connection to small scale science and technology because when characteristic flow length scales become of the order of, or smaller than, the molecular mean free path, the Navi...

The Runge–Kutta Discontinuous Galerkin Method for Conservation Laws V

This is the fifth paper in a series in which we construct and study the so-called Runge–Kutta discontinuous Galerkin method for numerically solving hyperbolic conservation laws. In this paper, we extend the method to multidimensional nonlinear systems of conservation laws. The algorithms are described and discussed, including algorithm formulation and practical implementation issues such as the...

The Runge-Kutta discontinuous Galerkin method for conservation laws V: . . .