A quadrature-free discontinuous Galerkin method for the level set equation

A quadrature-free discontinuous Galerkin method for the level set equation

A quadrature free, Runge–Kutta discontinuous Galerkin method (QF-RK-DGM) is developed to solve the level set equation written in a conservative form on twoand tri-dimensional unstructured grids. We show that the DGM implementation of the level set approach brings a lot of additional benefits as compared to traditional ENO level set realizations. Some examples of computations are provided that d...

A Level Set Discontinuous Galerkin Method for Free Surface Flows

We present a discontinuous Galerkin method on a fully unstructured grid for the modeling of unsteady incompressible fluid flows with free surfaces. The surface is modeled by embedding and represented by a levelset. We discuss the discretization of the flow equations and the level set equation as well a various ways of advancing the equations in time using velocity projection techniques. The eff...

Aiaa 9993309 Eecient Implementations of the Quadrature-free Discontinuous Galerkin Method Efficient Implementations of the Quadrature-free Discontinuous Galerkin Method

The e ciency of the quadrature-free form of the discontinuous Galerkin method in two dimensions, and brie y in three dimensions, is examined. Most of the work for constant-coe cient, linear problems involves the volume and edge integrations, and the transformation of information from the volume to the edges. These operations can be viewed as matrix-vector multiplications. Many of the matrices a...

An Application of the Quadrature-free Discontinuous Galerkin Method

The process of generating a block-structured mesh with the smoothness required for high-accuracy schemes is still a time-consuming process often measured in weeks or months. Unstructured grids about complex geometries are more easily generated, and for this reason, methods using unstructured grids have gained favor for aerodynamic analyses. The discontinuous Galerkin (DG) method is a compact ni...

A Discontinuous Spectral Element Method for the Level Set Equation