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首页> 外文期刊>International journal of numerical methods for heat & fluid flow >SLAC - a semi-Lagrangian artificial compressibility solver for steady-state incompressible flows
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SLAC - a semi-Lagrangian artificial compressibility solver for steady-state incompressible flows

机译：SLAC-半拉格朗日人工可压缩求解器，用于稳态不可压缩流

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Purpose The purpose of this paper is the development of a new density-based (DB) semi-Lagrangian method to speed up the conventional pressure-based (PB) semi-Lagrangian methods.Design/methodology/approach The semi-Lagrangian-based solvers are typically PB, i.e. semi-Lagrangian pressure-based (SLPB) solvers, where a Poisson equation is solved for obtaining the pressure field and ensuring a divergence-free flow field. As an elliptic-type equation, the Poisson equation often relies on an iterative solution, so it can create a challenge of parallel computing and a bottleneck of computing speed. This study proposes a new DB semi-Lagrangian method, i.e. the semi-Lagrangian artificial compressibility (SLAC), which replaces the Poisson equation by a hyperbolic continuity equation with an added artificial compressibility (AC) term, so a time-marching solution is possible. Without the Poisson equation, the proposed SLAC solver is faster, particularly for the cases with more computational cells, and better suited for parallel computing.Findings The study compares the accuracy and the computing speeds of both SLPB and SLAC solvers for the lid-driven cavity flow and the step-flow problems. It shows that the proposed SLAC solver is able to achieve the same results as the SLPB, whereas with a 3.03 times speed up before using the OpenMP parallelization and a 3.35 times speed up for the large grid number case (512 x 512) after the parallelization. The speed up can be improved further for larger cases because of increasing the condition number of the coefficient matrixes of the Poisson equation.Originality/value This paper proposes a method of avoiding solving the Poisson equation, a typical computing bottleneck for semi-Lagrangian-based fluid solvers by converting the conventional PB solver (SLPB) to the DB solver (SLAC) through the addition of the AC term. The method simplifies and facilitates the parallelization process of semi-Lagrangian-based fluid solvers for modern HPC infrastructures, such as OpenMP and GPU computing.
机译：目的本文的目的是开发一种新的基于密度（DB）的半拉格朗日方法，以加快传统的基于压力（PB）的半拉格朗日方法。设计/方法/方法基于半拉格朗日的求解器通常是PB，即基于半拉格朗日基于压力（SLPB）的求解器，在其中求解泊松方程以获得压力场并确保无散度的流场。作为椭圆型方程，泊松方程通常依赖于迭代解，因此可能会给并行计算带来挑战，并带来计算速度的瓶颈。这项研究提出了一种新的DB半拉格朗日方法，即半拉格朗日人工可压缩性（SLAC），该方法通过添加双曲线连续性方程的Poisson方程，并添加了人工可压缩性（AC）项，因此可以进行时间步解。没有Poisson方程，拟议中的SLAC求解器速度更快，尤其是在计算单元更多的情况下，并且更适合并行计算。研究比较了SLPB和SLAC求解器在盖驱动腔中的精度和计算速度流和分步流问题。结果表明，所提出的SLAC求解器能够实现与SLPB相同的结果，而在使用OpenMP并行化之前，速度提高了3.03倍；对于并行化之后的大网格数情况（512 x 512），速度提高了3.35倍。对于较大的情况，由于增加了泊松方程的系数矩阵的条件数，因此可以进一步提高速度。原始数据/值本文提出一种避免求解泊松方程的方法，这是基于半拉格朗日算法的典型计算瓶颈通过添加AC项将常规的PB求解器（SLPB）转换为DB求解器（SLAC）来实现流体求解器。该方法简化并促进了基于半拉格朗日流体求解器的并行化过程，用于现代HPC基础设施，例如OpenMP和GPU计算。

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