High order conservative finite difference scheme for variable density low Mach number turbulent flows
High order conservative finite difference scheme for variable density low Mach number turbulent flows
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DOI：
10.1016/j.jcp.2008.03.027
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发表时间：
2008-07-20
影响因子：
4.1
通讯作者：
Pitsch, Heinz
中科院分区：
文献类型：
--
作者：
Desjardins, Olivier;Blanquart, Guillaume;Pitsch, Heinz
Morinishi等人的高阶守恒型有限差分格式。作者声明：[Y.Morinishi，ON.Vasilyev，T.Ogi，柱坐标下不可压缩流动模拟的完全守恒有限差分格式，J.康普特。太棒了。197(2004)686]被推广到具有柱面或笛卡尔非均匀网格的复杂几何形状中的变密度流动的模拟。该公式在周期域中离散守恒质量、动量和动能。在有墙的情况下，得到了确保一级保护的边界条件，而二级保护显示仍然令人满意。在圆柱坐标的情况下，希望提高对流项在径向的精度阶数，因为在径向通常可以找到最大的梯度。采用了简单的中心线处理，导致了良好的准确性以及令人满意的稳健性。引入了一种类似的策略来提高粘性项的精度。该格式将任意高精度、离散的质量、动量和能量守恒与一致的边界条件结合在一起，非常适合于模拟实际几何形状的反应性湍流流动。用这种数值方法模拟了从各向同性湍流到变密度圆喷流的一系列正则湍流。给出了直接数值模拟和大涡模拟的结果。结果表明，高阶空间精度可以显著提高计算结果的质量。对几种情况下的误码率进行了详细分析。结果表明，高阶格式比低阶格式具有更高的计算效率。(C)2008 Elsevier Inc.保留所有权利。
The high order conservative finite difference scheme of Morinishi et al. [Y. Morinishi, ON. Vasilyev, T. Ogi, Fully conservative finite difference scheme in cylindrical coordinates for incompressible flow simulations, J. Comput. Phys. 197 (2004) 686] is extended to simulate variable density flows in complex geometries with cylindrical or cartesian non-uniform meshes. The formulation discretely conserves mass, momentum, and kinetic energy in a periodic domain. In the presence of walls, boundary conditions that ensure primary conservation have been derived, while secondary conservation is shown to remain satisfactory. In the case of cylindrical coordinates, it is desirable to increase the order of accuracy of the convective term in the radial direction, where most gradients are often found. A straightforward centerline treatment is employed, leading to good accuracy as well as satisfactory robustness. A similar strategy is introduced to increase the order of accuracy of the viscous terms. The overall numerical scheme obtained is highly suitable for the simulation of reactive turbulent flows in realistic geometries, for it combines arbitrarily high order of accuracy, discrete conservation of mass, momentum, and energy with consistent boundary conditions. This numerical methodology is used to simulate a series of canonical turbulent flows ranging from isotropic turbulence to a variable density round jet. Both direct numerical simulation (DNS) and large eddy simulation (LES) results are presented. It is observed that higher order spatial accuracy can improve significantly the quality of the results. The error to cost ratio is analyzed in details for a few cases. The results suggest that high order schemes can be more computationally efficient than low order schemes. (c) 2008 Elsevier Inc. All rights reserved.