A New Method for Approximating of First Derivatives in Smoothed Particle Hydrodynamics: Theory and Practice for Linear Transport Equation

• Published in: Lobachevskii journal of mathematics Vol. 46; no. 1; pp. 43 - 54
• Main Authors: Burmistrova, O. A., Markelova, T. V., Arendarenko, M. S., Stoyanovskaya, O. P.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.01.2025; Springer Nature B.V
• Subjects: Algebra; Analysis; Approximation; Computing costs; Derivatives; Fluid mechanics; Geometry; Mathematical Logic and Foundations; Mathematics; Mathematics and Statistics; Nodes; Partial differential equations; Probability Theory and Stochastic Processes; Smooth particle hydrodynamics; Transport equations; partial differential equation; high-order SPH method; approximate dispersion relation; 2010 Mathematics Subject Classification: 65M08; transport equation; dispersion analysis

Smoothed Particle Hydrodynamics (SPH) can be considered as a method for approximating dynamical partial differential equations on moving irregularly spaced nodes. The main idea of SPH is to construct a smooth approximating function for a discrete set of nodes using finite smoothing kernels whose sup...