一类新型自适应反扩散近似Riemann求解器及其应用  

A new type of approximate Riemann solver with adaptive anti-diffusion and its application

作　　者：刘旭亮[1,2] 范召林[2] 张树海[1,2] 李虎[1,2] 罗勇 孙晓峰[3] LIU Xuliang;FAN Zhaolin;ZHANG Shuhai;LI Hu;LUO Yong;SUN Xiaofeng(State Key Laboratory of Aerodynamics,China Aerodynamics Research and Development Center,Mianyang 621000,China;China Aerodynamics Research and Development Center,Mianyang 621000,China;School of Energy and Power Engineering,Beihang University,Beijing 100191,China)

机构地区：[1]中国空气动力研究与发展中心空气动力学国家重点实验室,绵阳621000 [2]中国空气动力研究与发展中心,绵阳621000 [3]北京航空航天大学能源与动力工程学院,北京100191

出　　处：《空气动力学学报》2023年第4期52-63,I0001,共13页Acta Aerodynamica Sinica

基　　金：国家自然科学基金(11972360,11732016);四川省科技计划(2018JZ0076);国家数值风洞工程。

摘　　要：对于包含激波、剪切层等复杂结构的流动问题,为了精确模拟剪切层等精细结构,且保证激波计算的稳定性,必须采用低耗散且强鲁棒的数值通量方法。传统的HLL近似Riemann求解器的耗散性较大,Roe、HLLEM和HLLC等近似Riemann求解器在计算某些含有强激波的物理问题时会出现非物理解,容易导致不稳定。针对这一问题,本文在Riemann求解器中通过合理设计反扩散矩阵,发展了一类具有自适应反扩散的新型Riemann求解器,并将其应用到高阶加权紧致格式,实现了高阶精度求解。通过典型数值算例验证了新型方法的计算精度和稳定性,结果表明本文提出的新型自适应反扩散Riemann求解器克服了传统Riemann求解器的缺陷,既能准确识别剪切层等精细结构,又能保证激波解的稳定性。Constructing numerical fluxes using Riemann solvers is one of the most important steps for solving hyperbolic systems of conservation laws.However,it is still of great challenge for existing Riemann solvers to simulate high-speed flows with shock waves.The Riemann solver based on the HLL approximation has a high dissipation,while those based on the Roe,HLLEM,and HLLC approximation may result in non-physical solutions and numerical instability when simulating complex flows with strong shock waves.Because of this,a new type of Riemann solver with adaptive anti-diffusion is developed by a dedicated design of the anti-diffusion matrix.Due to its low dissipation,the proposed Riemann solver yields high-accuracy solutions when applied to high-order weighted compact finite difference schemes.The standard numerical experiments verify computational accuracy and stability for the new method,which show that the new Riemann solver overcomes the shortcomings of the traditional approximate Riemann solver.The new Riemann solver can accurately identify the fine structures such as shear layers,and maintain the numerical stability for the computation of shock wave.

关 键 词：近似Riemann求解器 自适应反扩散 激波 高阶格式 数值稳定性 

分 类 号：O241.8[理学—计算数学]