A high-order Discontinuous Galerkin solver for the incompressible RANS and k–ω turbulence model equations
A high-order Discontinuous Galerkin solver for the incompressible RANS and k–ω turbulence model equations
复制标题
用于不可压缩 RANS 和 k-ω 湍流模型方程的高阶间断伽辽金求解器
DOI：
10.1016/j.compfluid.2014.02.028
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发表时间：
2014
影响因子：
2.8
通讯作者：
M. Savini
中科院分区：
文献类型：
--
作者：
F. Bassi;A. Ghidoni;Andrea Perbellini;S. Rebay;A. Crivellini;N. Franchina;M. Savini
本文将不可压缩Navier-Stokes方程的不连续Galerkin （DG）解算器推广到具有k -ω湍流模型的reynolds - average Navier-Stokes （RANS）方程。该方法的一个显著特点是基于具有松弛不可压缩约束的不可压缩欧拉方程的精确黎曼解的非粘界面数值通量的公式。湍流模型以非标准的方式实现，采用变量ω ~ = log ω代替ω，并强制满足模拟湍流应力的可实现条件。通过计算几个湍流测试案例，评估了所提出实现的可靠性、鲁棒性和准确性：(i)雷诺数Re= 11.1× 10.6时的平板流动，（ii）不同攻角α= 0°、10°、15°和雷诺数Re= 2.88× 10.6、6.0× 10.6时NACA 0012翼型周围的流动，并与实验和CFD基准数据进行了比较，以及（iii）通过旋转垂直轴风力机的流动。
In this work a Discontinuos Galerkin (DG) solver for the incompressible Navier–Stokes equations has been extended to deal with the Reynolds-Averaged Navier–Stokes (RANS) equations coupled with the k–ω turbulence model. A distinguishing feature of the method is the formulation of the inviscid interface numerical fluxes, based on an exact Riemann solver for the incompressible Euler equations with a relaxed incompressibility constraint. The turbulence model has been implemented in a non-standard way employing the variable ω∼= log ω instead of ω and enforcing the fulfilment of realizability conditions for the modeled turbulent stresses. The reliability, robustness and accuracy of the proposed implementation have been assessed by computing several turbulent test cases:(i) the flow past a flat plate for a Reynolds number Re= 11.1× 10 6,(ii) the flow around a NACA 0012 airfoil at different angles of attack α= 0°, 10°, 15° and Reynolds numbers Re= 2.88× 10 6, 6.0× 10 6, with comparisons with experimental and CFD benchmark data, and (iii) the flow through a rotating vertical axis wind turbine.