Coupling with the Embedded Boundary Method in a Runge-Kutta Discontinuous-Galerkin Direct Ghost-Fluid Method (RKDG-DGFM) Framework for Fluid-Structure Interaction Simulations of Underwater Explosions

A High Order Discontinuous Galerkin Method for Fluid-Structure Interaction

We describe a method for computing time-dependent solutions to the compressible Navier-Stokes equations coupled to a hyperelastic Neo-Hookean membrane model. The deforming domain is handled by introducing a continuous mapping between a fixed reference configuration and the time varying domain, and rewriting the Navier-Stokes equations as a conservation law for the independent variables in the r...

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...

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 ...

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: . . .