相关论文: Turbulent jet simulation using high-order DG metho…
In this paper, a uniformly high-order discontinuous Galerkin gas kinetic scheme (DG-HGKS) is proposed to solve the Euler equations of compressible flows. The new scheme is an extension of the one-stage compact and efficient high-order GKS…
Modern astrophysical simulations aim to accurately model an ever-growing array of physical processes, including the interaction of fluids with magnetic fields, under increasingly stringent performance and scalability requirements driven by…
In recent years, coupled with traditional turbulence models, the second-order gas-kinetic scheme (GKS) has been used in the turbulent flow simulations. At the same time, high-order GKS has been developed, such as the two-stage fourth-order…
A new high order accurate staggered semi-implicit space-time discontinuous Galerkin (DG) method is presented for the simulation of viscous incompressible flows on unstructured triangular grids in two space dimensions. The staggered DG…
The construction of discontinuous Galerkin (DG) methods for the compressible Euler or Navier-Stokes equations (NSE) includes the approximation of non-linear flux terms in the volume integrals. The terms can lead to aliasing and stability…
We are developing a new continuum gyrokinetic code, Gkeyll, for use in edge plasma simulations, and here present initial simulations of turbulence on open field lines with model sheath boundary conditions. The code implements an energy…
The Runge--Kutta discontinuous Galerkin (RKDG) method is a high-order technique for addressing hyperbolic conservation laws, which has been refined over recent decades and is effective in handling shock discontinuities. Despite its…
The discontinuous Galerkin (DG) method is an established method for computing approximate solutions of partial differential equations in many applications. Unlike continuous finite elements, in DG methods, numerical fluxes are used to…
We assess the ability of three different approaches based on high-order discontinuous Galerkin methods to simulate under-resolved turbulent flows. The capabilities of the mass conserving mixed stress method as structure resolving large eddy…
High-order methods are well-suited for the numerical simulation of complex compressible turbulent flows, but require additional stabilization techniques to capture instabilities arising from the underlying non-linear hyperbolic equations.…
A framework for performing dynamic mesh adaptation with the discontinuous Galerkin method (DGM) is presented. Adaptations include modifications of the local mesh step size (h-adaptation) and the local degree of the approximating polynomials…
Combustion instabilities are a major concern in the design of Liquid Rocket Engines (LREs) and gas turbines. During this PhD work, several directions were explored to understand and mitigate their effects. First, more efficient and robust…
In this paper, we propose an efficient high order semi-Lagrangian (SL) discontinuous Galerkin (DG) method for solving linear convection-diffusion equations. The method generalizes our previous work on developing the SLDG method for…
In this paper we propose and analyze finite element discontinuous Galerkin methods for the one- and two-dimensional stochastic Maxwell equations with multiplicative noise. The discrete energy law of the semi-discrete DG methods were…
In the present work, large-eddy simulations of free supersonic jet flows are performed to investigate the influence of inflow conditions on the jet flow field and its turbulent properties. A high-order nodal discontinuous Galerkin method is…
This work presents a numerical analysis of a Discontinuous Galerkin (DG) method for a transformed master equation modeling an open quantum system: a quantum sub-system interacting with a noisy environment. It is shown that the presented…
In this paper, we develop a class of high order conservative semi-Lagrangian (SL) discontinuous Galerkin (DG) methods for solving multi-dimensional linear transport equations. The methods rely on a characteristic Galerkin weak formulation,…
In this paper, we develop a sparse grid discontinuous Galerkin (DG) scheme for transport equations and applied it to kinetic simulations. The method uses the weak formulations of traditional Runge-Kutta DG (RKDG) schemes for hyperbolic…
In two and three dimension we analyze discontinuous Galerkin methods for the acoustic problem. The acoustic fluid that we consider on this paper is inviscid, leading to a linear eigenvalue problem. The acoustic problem is written, in first…
3D2V continuum gyrokinetic simulations of electrostatic plasma turbulence in a straight, open-field-line geometry have been performed using the full-$f$ discontinuous-Galerkin code Gkeyll. These simulations include the basic elements of a…