Efficient exploitation of exascale architectures requires rethinking of the numerical
algorithms used in many large-scale applications. These architectures favor algorithms that …

We study the stability and sensitivity of an absorbing layer for the Boltzmann equation by
examining the Bhatnagar–Gross–Krook (BGK) approximation and using the perfectly …

Simulations of the discrete Boltzmann Bhatnagar–Gross–Krook equation are an important
tool for understanding fluid dynamics in non-continuum regimes. Here, we introduce a …

In this paper we consider a level set reinitialization technique based on a high-order, local
discontinuous Galerkin method on unstructured triangular meshes. A finite volume based …

We present a GPU-accelerated method for large scale, coupled incompressible fluid flow
and heat transfer problems. A high-order, nodal discontinuous Galerkin method is utilized to …

This thesis explores the ability of the discontinuous Galerkin (DG) method to numerically
solve the Boltzmann equation. Constructing numerical methods for this equation is a …

Simulations of the discrete Boltzmann Bhatnagar-Gross-Krook (BGK) equation are an
important tool for understanding fluid dynamics in non-continuum regimes. Here, we …

The application of finite element method in solving the lattice Boltzmann equation has been
successfully demonstrated by many researchers. However, the computation cost of these …

This thesis advances the understanding and computational techniques of low Mach number
aerodynamics by applying high-order discontinuous Galerkin (DG) solutions to the …

This thesis focuses on creating high-order discontinuous Galerkin approaches to solve
Level Set reinitialization problems utilizing Finite Volume-Subcell stabilization. Instead of …