运动粒子半隐式方法中拉普拉斯算子的泰勒一致离散化

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2025-08-08 DOI:10.1016/j.cam.2025.117000

Stephen Miller , Emiliano Renzi , Marco Discacciati

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引用次数: 0

摘要

我们推导了一种新的拉普拉斯近似用于运动粒子半隐式方法，保证了基于泰勒展开的严格的数学基础。通过研究该数值近似在均匀粒子排列和摄动粒子排列情况下的收敛速度，以及在求解具有不同边界条件的泊松问题时的收敛速度，比较了该方法的准确性。与以前的技术相比，所提出的模型更容易实现，并且总是保证至少一阶的准确性。

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Taylor consistent discretisation of the Laplace operator in the Moving Particle Semi-implicit method

We derive a new Laplacian approximation for use in the Moving Particle Semi-Implicit method, ensuring a rigorous mathematical foundation based on Taylor expansion. The accuracy of this novel approximation is evaluated through comparison with other existing methods by studying the convergence rate of the numerical approximation in uniform and perturbed particle arrangements, and when solving a Poisson problem with different types of boundary conditions. The proposed model allows for easier implementation with respect to previous techniques, and always guarantees an accuracy of at least first order.

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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.