求解RANS方程的高阶间断Galerkin方法研究

Exploring High-Order Accurate Discontinuous Galerkin Method for Numerical Solution of Compressible Reynolds-Averaged Navier-Stokes(RANS) Equations

基于二维结构网格,对间断Galerkin方法(DGM)求解雷诺平均Navier-Stokes(RANS)方程进行了研究。根据混合有限元方法的思想,引入辅助变量,对粘性项中的高阶导数项进行降阶处理,再应用DGM对辅助变量方程和降阶后的RANS方程进行联立求解。对平板层流流动进行了数值模拟,结果表明,随着逼近多项式次数的增加,速度型和摩擦系数更加接近Blasius解。此外,还引入了Bald-win-Lomax湍流模型,对NACA0012翼型跨音速粘性流场进行了数值模拟,与实验结果进行了对比,进一步验证了算法的可靠性。

Sections 1 and 2 of the full paper explain the exploration mentioned in the title. Section 1 gives quite de- tailed explanation of two-step discretization ; its core consists of： （ 1 ） with the mixed finite element method, we add an unknown variable to reduce the number of orders of the second-order derivatives of viscous terms; （2） we carry out the discontinuous Galerkin discretization of the RANS equations whose orders have been reduced. Section 2 is entitled ＂numerical results and their analysis＂ ; its core consists of： （ 1 ） we carry out the numerical simulation of the laminar flow over a flat plate; （2） we use the Baldwin-Lomax turbulence model and the moment limiter to sim- ulate the transonic viscous flow field over NACA0012 airfoil; the simulation results, presented in Figs. 1 through 8, and their comparison with the available experimental data show preliminarily that our discontinuous Galerkin method can indeed solve the RANS equations satisfactorily and that the simulation results agree reasonably well with the experiment data.