Abstract Two algorithms for a fast Cartesian mesh-based flow simulation over complex geometries are presented. As a first category, a geometric multigrid (MG) method using direct restriction of the Heaviside function, which is 0 in the body and 1 in the fluid, is presented. This method is easy to implement, readily parallelizable, and can be applied to any irregular domain. The validity and optimal performance of the current MG method are demonstrated by solving an analytically defined Poisson problem on an irregular domain. Another part of this paper is to introduce a novel efficient method for computing the signed distance function (SDF), which is a typical level-set value to represent bodies on Cartesian meshes. In the Cartesian mesh-based simulation, only the SDF near the body interface is accurately required. Based on this fact, the number of operations for computing the SDF can be significantly reduced by focusing on interface cells. In this study, the adaptive mesh refinement (AMR) strategy is employed to effectively trace the interface cells. By using these two algorithms, an in-house Cartesian mesh-based incompressible flow solver is developed. To demonstrate the applicability of the current approaches, well-known benchmark problems in 2D and 3D are simulated. Finally, as the most challenging case, simulations for flow over an underwater robot, namely Crabster, are presented.

中文翻译：

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复杂几何图形上的几何多重网格加速不可压缩流动模拟

摘要 提出了在复杂几何结构上进行基于笛卡尔网格的快速流动模拟的两种算法。作为第一类，提出了使用 Heaviside 函数的直接约束的几何多重网格 (MG) 方法，该函数在体内为 0，在流体中为 1。这种方法易于实现，易于并行化，并且可以应用于任何不规则域。通过在不规则域上求解解析定义的泊松问题，证明了当前 MG 方法的有效性和最佳性能。本文的另一部分是介绍一种计算有符号距离函数 (SDF) 的新方法，它是在笛卡尔网格上表示物体的典型水平集值。在基于笛卡尔网格的模拟中，只需要精确地要求身体界面附近的 SDF。基于这个事实，通过关注接口单元，可以显着减少计算 SDF 的操作次数。在这项研究中，自适应网格细化（AMR）策略被用来有效地追踪界面单元。通过使用这两种算法，开发了内部基于笛卡尔网格的不可压缩流动求解器。为了证明当前方法的适用性，模拟了 2D 和 3D 中众所周知的基准问题。最后，作为最具挑战性的案例，介绍了水下机器人（即 Crabster）上的流动模拟。内部开发了基于笛卡尔网格的不可压缩流动求解器。为了证明当前方法的适用性，模拟了 2D 和 3D 中众所周知的基准问题。最后，作为最具挑战性的案例，介绍了水下机器人（即 Crabster）上的流动模拟。内部开发了基于笛卡尔网格的不可压缩流动求解器。为了证明当前方法的适用性，模拟了 2D 和 3D 中众所周知的基准问题。最后，作为最具挑战性的案例，介绍了水下机器人（即 Crabster）上的流动模拟。