Abstract
In this paper, a high-resolution front tracking method was presented for interface tracking simulation with Runge-Kutta discontinuous Galerkin methods. An interface treating method of the discontinuous methods is presented. This method don’t construct the ghost fluid and the flow information on both sides next to the interface is used to solve the interfacial status. The limiter adopted the combination of the shock detection and monotonicity-preserving limiter and level set method is used for tracking the interface. Result shown that the front tracking of the high-order accurate Runge-Kutta discontinuous Galerkin method exhibits very good agreement with exact solution in the interface condition that contain strong shock.
Highlights
The treatment of moving interfaces and their vicinity field is crucial in multi-medium flow simulation due to its discontinuous contact
These types of methods can be separated into two categories by how each considers the interfaces: diffuse interface method (DIM) and sharp interface method (SIM)
Cockbum et al established a framework for nonlinear time dependent hyperbolic conservation law, using nonlinearly stable high order Runge-Kutta time discretization [8], discontinuous Galerkin discretization in space with Riemann solvers as numerical fluxes and total variation bounded nonlinear limiter [9], to achieve nonoscillatory properties in condition of strong shocks
Summary
The treatment of moving interfaces and their vicinity field is crucial in multi-medium flow simulation due to its discontinuous contact. These types of methods can be separated into two categories by how each considers the interfaces: diffuse interface method (DIM) and sharp interface method (SIM). Cockbum et al established a framework for nonlinear time dependent hyperbolic conservation law, using nonlinearly stable high order Runge-Kutta time discretization [8], discontinuous Galerkin discretization in space with Riemann solvers as numerical fluxes and total variation bounded nonlinear limiter [9], to achieve nonoscillatory properties in condition of strong shocks. There are many limiters [14,22,23,24] ,and in this article, the limiter adopted the combination of the shock detection and monotonicity-preserving limiter
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