曲线网格下带有自由流和涡流保存特性的低耗散数值方案  

A low-dissipation WENO-THINC scheme for freestream and vortex preservation on general curvilinear grids

作　　者：李晶琦 刘成 高若青 胡长洪 Jingqi Li;Cheng Liu;Ruoqing Gaol;Changhong Hu(School of Naval Architecture,Ocean and Civil Engineering,Shanghai Jiao Tong University,Shanghai 200240,China;Research Institute for Applied Mechanics,Kyushu University,Fukuoka 816-0811,Japan)

机构地区：[1]School of Naval Architecture,Ocean and Civil Engineering,Shanghai Jiao Tong University,Shanghai 200240,China [2]Research Institute for Applied Mechanics,Kyushu University,Fukuoka 816-0811,Japan

出　　处：《Acta Mechanica Sinica》2023年第7期152-172,共21页力学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.51979160,11902199).

摘　　要：本文提出了一种改进的THINC数值方案,用于在曲线网格下保持自由来流和等熵涡特性,其中采用对称保守度量方法来消除坐标转换系数在数值离散中诱导的几何误差.由于非等间距的网格会导致原本带有固定陡度参数的THINC方案的数值精度和计算稳定性降低.因此,本文引入了一种带有自适应陡度参数的THINC方案用于减少数值耗散,其中陡度参数根据网格间隔的大小建立方程实现自适应缩放.数值测试表明,与原始THINC方案相比,新的THINC方案能够有效地在一般结构化曲线网格下保持自由流和涡旋保存,并且能够更加精准地拟合流场中的各类型间断和小尺度结构.此外,通过边界变差最小(BVD)原理,将改进的THINC方案与加权本质非振荡方案(WENO)相结合,兼顾了光滑解和间断解的数值精度.本文在波浪形网格和随机网格下设置了一系列一维和二维数值算例,分别测试了在有限差分和有限体积框架下改进的THINC方法与低耗散的WENO-THINC综合方案的性能.数值验证结果表明改进后的数值方案可以有效地减少非物理振荡和数值耗散,相较于原始方案和同类型数值方案有较明显的优势.In this paper,we present a modified tangent of hyperbola for interface capturing(THINC)scheme for freestream and vortex preservation on the general curvilinear grids,in which the symmetric conservative metric method is employed to eliminate the geometrical errors in the discretization of Jacobian and the metrics.As the original THINC with a fixed jump steepness may lose accuracy and result in instability problem on non-uniform grids,a new algorithm is introduced to reduce the numerical dissipation,in which the jump steepness is scaled adaptively according to varying mesh intervals.Numerical tests show the new THINC scheme can hold freestream and vortex preservation and is capable of resolving discontinuities and small-scale smooth flow structures with less dissipation on general curvilinear grids,compared with the original THINC.By using the boundary variation diminishing(BVD)principle,the modified THINC is implemented in combination with a finite-difference weighted essentially non-oscillatory(WENO)scheme.Comprehensive numerical validations are performed to evaluate the performance of the improved THINC and WENO combined with the modified THINC in the framework of both the FDM and FVM,with twisting and even randomly spaced curvilinear meshes.Numerical results of the double Mach reflection also demonstrate the improved THINC can alleviate non-physical oscillations with less numerical dissipation.

关 键 词：数值精度 曲线网格 数值耗散 转换系数 非等间距 几何误差 波浪形 数值离散 

分 类 号：O3[理学—力学]