A discontinuous Galerkin method with plane waves and Lagrange multipliers for the solution of short wave exterior Helmholtz problems on unstructured meshes

Wave Motion ◽  
2004 ◽  
Vol 39 (4) ◽  
pp. 307-317 ◽  
Author(s):  
Charbel Farhat ◽  
Paul Wiedemann-Goiran ◽  
Radek Tezaur
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Lagrange Multipliers ◽  
Plane Waves ◽  
Unstructured Meshes ◽  
Short Wave

Runge-Kutta Discontinuous Galerkin Method with Front Tracking Method for Solving the Compressible Two-Medium Flow on Unstructured Meshes

2016 ◽  
Vol 9 (1) ◽  
pp. 73-91 ◽  
Author(s):  
Haitian Lu ◽  
Jun Zhu ◽  
Chunwu Wang ◽  
Ning Zhao
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Front Tracking ◽  
Unstructured Meshes ◽  
Interfacial Region ◽  
Tracking Method ◽  
Front Tracking Method ◽  
Medium Flow ◽  
Runge Kutta

AbstractIn this paper, we extend using the Runge-Kutta discontinuous Galerkin method together with the front tracking method to simulate the compressible two-medium flow on unstructured meshes. A Riemann problem is constructed in the normal direction in the material interfacial region, with the goal of obtaining a compact, robust and efficient procedure to track the explicit sharp interface precisely. Extensive numerical tests including the gas-gas and gas-liquid flows are provided to show the proposed methodologies possess the capability of enhancing the resolutions nearby the discontinuities inside of the single medium flow and the interfacial vicinities of the two-medium flow in many occasions.

Multiple-Stencil Dispersion Analysis of the Lagrange Multipliers in a Discontinuous Galerkin Method for the Helmholtz Equation

2003 ◽  
Vol 11 (02) ◽  
pp. 239-254 ◽  
Author(s):  
Isaac Harari ◽  
Charbel Farhat ◽  
Ulrich Hetmaniuk
Keyword(s):  
Helmholtz Equation ◽  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Lagrange Multiplier ◽  
Lagrange Multipliers ◽  
Degrees Of Freedom ◽  
Dispersion Analysis ◽  
Dispersion Properties

We analyze the dispersion properties of elements obtained by a discontinuous Galerkin method with Lagrange multipliers. The dispersion analysis of these elements presents a challenge in that the Lagrange multiplier degrees of freedom are directional, and hence an unbounded mesh is made up of more than one repeating pattern. Two approaches to overcome this difficulty are presented. The similarity in the two sets of results offers mutual validation of the two approaches.

Sign in / Sign up

Export Citation Format

Share Document