Semi‐implicit Lagrangian Voronoi approximation for the incompressible Navier–Stokes equations

IF 1.7 4区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Ondřej Kincl, Ilya Peshkov, Walter Boscheri
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引用次数: 0

Abstract

We introduce semi‐implicit Lagrangian Voronoi approximation (SILVA), a novel numerical method for the solution of the incompressible Euler and Navier–Stokes equations, which combines the efficiency of semi‐implicit time marching schemes with the robustness of time‐dependent Voronoi tessellations. In SILVA, the numerical solution is stored at particles, which move with the fluid velocity and also play the role of the generators of the computational mesh. The Voronoi mesh is rapidly regenerated at each time step, allowing large deformations with topology changes. As opposed to the reconnection‐based Arbitrary‐Lagrangian‐Eulerian schemes, we need no remapping stage. A semi‐implicit scheme is devised in the context of moving Voronoi meshes to project the velocity field onto a divergence‐free manifold. We validate SILVA by illustrative benchmarks, including viscous, inviscid, and multi‐phase flows. Compared to its closest competitor, the Incompressible Smoothed Particle Hydrodynamics method, SILVA offers a sparser stiffness matrix and facilitates the implementation of no‐slip and free‐slip boundary conditions.
不可压缩纳维-斯托克斯方程的半隐式拉格朗日 Voronoi 近似法
我们介绍了半隐式拉格朗日 Voronoi 近似(SILVA),这是一种用于求解不可压缩欧拉方程和纳维-斯托克斯方程的新型数值方法,它结合了半隐式时间行进方案的高效性和随时间变化的 Voronoi 网格的鲁棒性。在 SILVA 中,数值解存储在粒子中,粒子随流体速度移动,同时也是计算网格的生成器。在每个时间步长内,Voronoi 网格都会快速再生,从而允许随着拓扑结构的变化而产生较大的变形。与基于重连接的任意-拉格朗日-欧拉方案不同,我们不需要重映射阶段。在移动 Voronoi 网格的背景下,我们设计了一种半隐式方案,将速度场投影到无发散流形上。我们通过粘性流、不粘性流和多相流等说明性基准验证了 SILVA。与其最接近的竞争对手--不可压缩平滑粒子流体力学方法相比,SILVA 提供了更稀疏的刚度矩阵,并便于实施无滑动和自由滑动边界条件。
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来源期刊
International Journal for Numerical Methods in Fluids
International Journal for Numerical Methods in Fluids 物理-计算机:跨学科应用
CiteScore
3.70
自引率
5.60%
发文量
111
审稿时长
8 months
期刊介绍: The International Journal for Numerical Methods in Fluids publishes refereed papers describing significant developments in computational methods that are applicable to scientific and engineering problems in fluid mechanics, fluid dynamics, micro and bio fluidics, and fluid-structure interaction. Numerical methods for solving ancillary equations, such as transport and advection and diffusion, are also relevant. The Editors encourage contributions in the areas of multi-physics, multi-disciplinary and multi-scale problems involving fluid subsystems, verification and validation, uncertainty quantification, and model reduction. Numerical examples that illustrate the described methods or their accuracy are in general expected. Discussions of papers already in print are also considered. However, papers dealing strictly with applications of existing methods or dealing with areas of research that are not deemed to be cutting edge by the Editors will not be considered for review. The journal publishes full-length papers, which should normally be less than 25 journal pages in length. Two-part papers are discouraged unless considered necessary by the Editors.
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