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A DGBGK scheme based on WENO limiters for viscous and inviscid flows

机译：基于WENO限制器的DGBGK方案，用于粘性和非粘性流

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摘要

This paper presents a discontinuous Galerkin BGK (DGBGK) method for both viscous and inviscid flow simulations under a DG framework with a gas-kinetic flux and WENO limiters. In the DGBGK method, the construction of the flux in the DG method is based on the particle transport and collisional mechanism which not only couples the convective and dissipative terms together, but also includes both discontinuous and continuous terms in the flux formulation. Due to the connection between the gas-kinetic BGK model and the Euler as well as the Navier-Stokes equations, both viscous and inviscid flow equations can be simulated by a unified formulation. WENO limiters are used to obtain uniform high-order accuracy and sharp non-oscillatory shock transition. In the current method, the time accuracy is achieved by the direct integration of both time-dependent flux function at a cell interface and the flow variables inside each element. Numerical examples in one and two space dimensions are presented to illustrate the robustness and accuracy of the present scheme. (c) 2008 Elsevier Inc. All rights reserved.
机译：本文提出了一种不连续的Galerkin BGK（DGBGK）方法，该方法用于在具有气体动力学通量和WENO限制器的DG框架下进行粘性和非粘性流动模拟。在DGBGK方法中，DG方法中通量的构建基于粒子传输和碰撞机制，该机制不仅将对流项和耗散项耦合在一起，而且在通量公式中还包括不连续项和连续项。由于气体动力学BGK模型与Euler方程以及Navier-Stokes方程之间的联系，因此可以通过统一的公式模拟粘性和非粘性流动方程。 WENO限幅器用于获得一致的高阶精度和尖锐的非振荡冲击过渡。在当前方法中，时间精度是通过直接将单元界面上随时间变化的流量函数与每个元素内部的流量变量直接集成在一起而实现的。给出了在一维和二维空间中的数值示例，以说明本方案的鲁棒性和准确性。 （c）2008 Elsevier Inc.保留所有权利。

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