A well balanced diffuse interface method for complex nonhydrostatic free surface flows
A well balanced diffuse interface method for complex nonhydrostatic free surface flows
复制标题
DOI：
10.1016/j.compfluid.2018.08.013
复制
发表时间：
2018-06
影响因子：
2.8
通讯作者：
Elena Gaburro;M. Castro;M. Dumbser
中科院分区：
文献类型：
--
作者：
Elena Gaburro;M. Castro;M. Dumbser
本文提出了一种有效的二阶精度平衡有限体积法，它借助于简单的扩散界面法来模拟复杂的自由表面流动。所采用的物理模型是一个两相模型，直接从可压缩多相流的Baer-Nunziato系统。特别地，如在[1]中首次提出的，通过假设气体相对于大气参考压力的相对压力为零，并且气体动量与液体动量相比可以忽略不计，方程的数量从七个减少到三个。两相模型不作任何浅水型系统的经典假设，因此不忽略垂向加速度，自由表面也不被约束为单值函数，因此即使是破碎波这样的复杂形状也能被正确地捕捉到.所得到的偏微分方程系统在结构化笛卡尔网格上用一种新的平衡良好的二阶精度路径守恒有限体积法求解，即使在存在障碍物的情况下也能够精确地保持平衡状态。此外，它自动计算的水-空气界面的位置，并确保在自由表面的低数值耗散由于一种新的Osher-Romberg型近似黎曼求解器。最后，高计算性能是由基于GPU的平台上的高效并行实现保证的，该平台达到每秒处理两千万卷的效率，并且可以采用非常精细的网格。我们的新的良好平衡的计划进行了验证，通过比较现有的分析，数值和实验参考解决方案的大量的测试情况下，其中振荡椭圆形滴，溃坝问题，破碎波，越顶堰流，和波浪冲击问题的数值结果。
In this paper we propose an efficient second order accurate well balanced finite volume method for modeling complex free surface flows at the aid of a simplediffuse interface method. The employed physical model is a two-phase model directly derived from the Baer–Nunziato system for compressible multi-phase flows. In particular, as proposed for the first time in [1], the number of equations is reduced from seven to three by assuming that the relative pressure of the gas with respect to the atmospheric reference pressure is zero, and that the gas momentum is negligible compared to the one of the liquid. The two-phase model does not make any of the classical assumptions of shallow water type systems, hence it doesnotneglect vertical accelerations and the free surface isnotconstraint to be a single-valued function, so evencomplexshapes as those of breaking waves can be properly captured.The resulting PDE system is solved by a novelwell balancedsecond order accurate path-conservative finite volume method on structured Cartesian grids, which is able to preserveexactlythe equilibrium states even in the presence of obstacles. It furthermore automatically computes the location of the water-air interfaces, and assures low numerical dissipation at the free surface thanks to a novel Osher-Romberg-type approximate Riemann solver. Finally, high computational performance is guaranteed by an efficientparallelimplementation on a GPU-based platform that reaches the efficiency of twenty million of volumes processed per seconds and makes it possible to employ even very fine meshes. The validation of our new well balanced scheme is carried out by comparing the obtained numerical results against existing analytical, numerical and experimental reference solutions for a large number of test cases, among which oscillating elliptical drops, dambreak problems, breaking waves, over topping weir flows, and wave impact problems.