摘要
提出了一种基于物面弱边界条件的Navier-Stokes方程并行全隐式求解方法。首先,实现了非结构网格格点格式有限体积法的粘性物面弱边界条件。以此为基础,推导了相应的粘性Jacobian矩阵。相比传统的物面强边界条件,弱边界条件的应用简化了该推导过程。接着,为了解决Spalart-Allmaras(S-A)模型的收敛和保正性问题,提出了基于物面弱边界条件的S-A模型无条件保正性收敛方法,通过构造特别的隐式矩阵同时保证S-A模型的收敛和湍流工作变量的正值。流场方程全隐式时间推进和无条件保正性收敛方法所得到的线性方程组采用多色高斯-塞德尔迭代法进行求解,并由MPI实现并行化。通过若干二维和三维算例对本文所提出的方法进行了测试,其结果表明:1)随着罚系数的增大,基于弱边界条件的结果趋向于基于强边界条件的结果;2)对于力的计算,弱边界条件自动满足通量一致关系而无需特别处理。
A parallel full implicit Navier-Stokes solver based on weakly imposed wall boundary condition is proposed.F irst,a weak boundary procedure for viscous solid wall is implemented on the unstructured node-centered finite volume method.Upon this procedure,the corresponding viscous Jacobian is derived.Compared to the traditional strongly imposed wall boundary condition,the application of weakly imposed boundary condition eases the derivation.To address the issues of convergence and positivity preserving difficulties with regard to the Spalart-Allmaras(S-A)m odel,an unconditionally positive-convergent(U PC)implicit schemefor the S-A model using weakly imposed wall boundary condition is presented,which is based on the construction of a special implicit matrix to ensure both the convergence of the S-A model and the positivity of the turbulence working variables.The linear equations resulted from the full implicit time integration and the UPC scheme are solved using multicolor Gauss-Seidel iteration(MCGS)and MPI is employed for parallelization.The proposed approach is tested by simulating several two-dimensional and three-dimensional cases.Results from the numerical simulations demonstrate th a t:1)with larger penalty strength param eter,the results of weak boundary conditions tend to those of strong boundary conditions;2)the weak boundary conditions satisfyflux consistency for force computation autom atically,and therefore no special treatm ent is required.
作者
高宜胜
伍贻兆
夏健
徐兆可
Gao Yisheng;Wu Yizhao;Xia Jian;Xu Zhaoke
出处
《空气动力学学报》
CSCD
北大核心
2017年第1期46-56,共11页
Acta Aerodynamica Sinica
基金
江苏高校优势学科建设工程资助项目(PAPD)
