CONVERGENCE OF THE SMOOTHED PARTICLE HYDRODYNAMICS METHOD FOR A SPECIFIC BAROTROPIC FLUID FLOW: CONSTRUCTIVE KERNEL THEORY
CONVERGENCE OF THE SMOOTHED PARTICLE HYDRODYNAMICS METHOD FOR A SPECIFIC BAROTROPIC FLUID FLOW: CONSTRUCTIVE KERNEL THEORY
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DOI：
10.1137/17m1157696
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发表时间：
2018-01-01
影响因子：
2
通讯作者：
Wendland, Holger
中科院分区：
文献类型：
--
作者：
Franz, Tino;Wendland, Holger
光滑粒子流体动力学（SPH）是一种基于粒子和核的流体流动数值计算方法。本文研究了一类正压流体欧拉方程的SPH方法的收敛性。与以往的工作相比，我们仔细区分平滑和离散参数，并给出明确的关系，他们之间的收敛性保证。这种收敛很大程度上取决于底层内核的某些属性。因此，本文的很大一部分是致力于建设紧支撑，径向核具有所需的属性。
Smoothed particle hydrodynamics (SPH) is a popular particle- and kernel-based method for numerically computing solutions to fluid-flow problems. In this paper, we study the convergence of SPH for the Euler equations of a specific barotropic fluid. In contrast to previous works, we distinguish carefully between the smoothing and the discretization parameters and give explicit relations between both of them to guarantee convergence. This convergence heavily depends on certain properties of the underlying kernel. Hence, a large part of this paper is devoted to constructing compactly supported, radial kernels which possess the required properties.