Improving accuracy of the moving grid particle finite element method via a scheme based on Strang splitting

• Published in: Computer methods in applied mechanics and engineering Vol. 369; p. 113212
• Main Authors: Marti, J., Ryzhakov, P.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01-09-2020; Elsevier BV
• Subjects: Accuracy; Computational fluid dynamics; Computer simulation; Finite element analysis; Finite element method; Fluid flow; Free-surface flows; Incompressible flow; Incompressible Navier–Stokes; Lagrangian; Mathematical analysis; PFEM; Software; Splitting; Strang splitting; Lagrangian; PFEM; Incompressible Navier–Stokes; Free-surface flows; Strang splitting
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2020.113212

Particle finite element method (PFEM) is a computational tool suitable for simulating fluid dynamics problems characterized by presence of moving boundaries. In this paper a new version of the method for incompressible flow problems is proposed aiming at accuracy improvement. This goal is achieved essentially by applying Strang operator splitting to Navier–Stokes equations and selecting adequate integration schemes for the resulting advective and Stokes sub-problems. For achieving efficient implementation, the pressure and the velocity in the Stokes part are decoupled via the fractional step technique as in the classical PFEM. However, at the first fractional step an explicit pressure prediction procedure for alleviating mass losses is introduced. Three test cases are solved, validating the methodology and estimating its accuracy. The numerical evidence proves that the proposed scheme improves the accuracy of the PFEM.