基于任意多面体网格的Navier-Stokes方程并行求解器

发展了一种基于任意多面体网格的Navier-Stokes(NS)方程并行求解器,基于积分守恒形式NS方程组,发展了支持任意多面体网格的中心有限体积方法。采用基于面的连接关系,对不同拓扑类型的网格如结构网格、非结构混合网格、多面体网格及剪切六面体(TRIMMER)网格]进行统一处理。对于无黏通量空间离散格式采用HLLEW(Harten-Lax-Van Leer-Einfeldt-Wada)格式,湍流模型采用k-ω两方程模型,时间推进采用适合并行计算的DP-LUR(data-parallel lower-upper relaxation)格式的隐式算法。对RAE2822翼型和ONERA M6机翼的结构网格、混合网格、多面体网格及TRIMMER网格进行了对比验证,结果表明发展的求解器具有较好的网格普适性,在不同拓扑类型的网格上均能求得较为接近实验值的结果;对多面体网格测试了加速比和并行效率,并行计算大大提高了计算效率。证明了求解器具有宽广的网格适应性,能够较为稳定、快速、准确地模拟定常绕流问题。

A PARALLEL SOLVER FOR NAVIER-STOKES EQUATION BASED ON ARBITRARY POLYHEDRAL GRIDS

A parallel solver for NS(Navier-Stokes) equations is developed based on arbitrary polyhedral grids. The central finite volume method is promoted based on integral conservation form NS equations, adaptive to arbitrary polyhedral grids. Grids of different topological types are implemented uniformly by introducing face-based connectivity, such as structural grids, hybrid grids, polyhedral grids and TRIMMER grids. The HLLEW scheme is applied for spatial discretization of the inviscid fluxes, and two equations turbulence models are used for the simulation of turbulent flows. The implicit time-marching method using DP-LUR(Data-Parallel Lower-Upper-Relaxation) is considered to improve the parallel computation. The comparison of structured grid, hybrid grid, polyhedral grid and TRIMMER grid for RAE2822 aerofoil is validated. It is shown that the results of different grids are closer to the experimental values, and that the solver in this paper has good universality in grids. The speed-up ratio and parallel efficiency are tested in TRIMMER mesh. It is demonstrated that parallel calculation could improve greatly calculation efficiency. Thus it is proved that the solver in this paper are stable, fast and accurate while exhibiting good adaptability on mesh topology.