可压缩流体高阶谱体积气体动理学格式
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- 英文论文题名：Spectral Volume Gas-kinetic Scheme for One-and Two-dimensional Flow Simulation
- 论文作者：刘娜 ; 汤华中
- 英文论文作者：Na Liu ; Huazhong Tang ; Institute of Applied Physics and Computational Mathematics ; Software Center for High Performance Numerical Simulation ; Laboratory of Computational Physics ; School of Mathematical Sciences ; Peking University
- 年：2016
- 作者机构：北京应用物理与计算数学研究所;中物院高性能数值模拟软件中心;计算物理重点实验室;北京大学数学科学学院;
- 论文关键词：谱体积气体动理学格式 ; BGK模型 ; 模板紧致 ; PFGM限制器
- 英文论文关键词：spectral volume gas-kinetic scheme ; BGK model ; compact stencil ; PFGM limiter
- 会议召开时间：2016-09-04
- 会议录名称：2016海峡两岸流体力学研讨会论文摘要集
- 语种：中文
- 分类号：O35
- 学会代码：AGLU
- 会议名称：2016海峡两岸流体力学研讨会
- 会议地点：中国青海西宁
- 主办单位：中国力学学会
- 学会名称：中国力学学会
- 页数：2
- 文件大小：4690k
- 原文格式：D
- 会议级别：全国
摘要
本文提出了一种求解可压缩流体的模板紧致的高精度动理学格式,称为高阶谱体积气体动理学格式(SVGKS)。以k阶SVGKS为例,将计算区域划分为若干谱体积元,再将谱体积元进一步划分为k个控制体或单元(例如通过在谱体积元内选择高斯点等)。在SVGKS中,当落在谱体积元内部的控制体界面处的流体状态连续时,数值通量就取为连续通量(通过连续的速度分布函数确定),故可简化计算并节省计算量;谱体积元内的解的重构中,由谱体积元内的控制体的单元平均值重构出该谱体积元中的高阶多项式,它在谱体积元的界面处一般是不连续的,但在落在谱体积元内部的控制体界面处是连续的。为了避免数值振荡,我们需要对谱体积元内重构的多项式进行判别和限制,首先用修正的TVB minmod函数识别"坏单元",然后对"坏单元"上重构的多项式函数使用PFGM限制器进行限制,也就是说只是对局部控制体("坏单元")使用限制器。几个一维和二维数值试验结果表明,格式对光滑解算例可以测得相应精度,对求解包含间断的问题也很有效,分辨率高,且节约计算量。
In this paper we combine the spectral volume method with the gas kinetic schemes and develop a high-order accurate spectral volume gas-kinetic scheme. Take the kth order accurate scheme as an example, the computational domain is first divided into spectral volumes and then each of them is further subdivided into k control volumes(e.g. by choosing Gauss points within each spectral volume). When the fluid state across the interface of the control volume in the spectral volume are continuous, numerical flux is taken as a continuous one, in which way it can simplify the calculation and save computation cost. The high order polynomial in the spectral volume is reconstructed by the cell average values over the control volumes within the spectral volume. It is generally not continuous across the interface of the spectral volume, but it is continuous across the interface of the control volume in the spectral volume. To avoid numerical oscillation, the reconstructed polynomial in the spectral volume need to be detected and limited, which means the limiter is used locally, not in all control volumes. A modified TVB minmod function is first used to identify the "troubled"cells and the PFGM limiter is then used in the "troubled"cells. Several one-and two-dimensional cases are tested and the results demonstrate that the kth order accurate spectral volume gas-kinetic scheme has kth order accuracy and is also efficient for solving problems with discontinuities.
In this paper we combine the spectral volume method with the gas kinetic schemes and develop a high-order accurate spectral volume gas-kinetic scheme. Take the kth order accurate scheme as an example, the computational domain is first divided into spectral volumes and then each of them is further subdivided into k control volumes(e.g. by choosing Gauss points within each spectral volume). When the fluid state across the interface of the control volume in the spectral volume are continuous, numerical flux is taken as a continuous one, in which way it can simplify the calculation and save computation cost. The high order polynomial in the spectral volume is reconstructed by the cell average values over the control volumes within the spectral volume. It is generally not continuous across the interface of the spectral volume, but it is continuous across the interface of the control volume in the spectral volume. To avoid numerical oscillation, the reconstructed polynomial in the spectral volume need to be detected and limited, which means the limiter is used locally, not in all control volumes. A modified TVB minmod function is first used to identify the "troubled"cells and the PFGM limiter is then used in the "troubled"cells. Several one-and two-dimensional cases are tested and the results demonstrate that the kth order accurate spectral volume gas-kinetic scheme has kth order accuracy and is also efficient for solving problems with discontinuities.
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