Smoothing algorithm for stabilization of the material point method for fluid–solid interaction problems

• Published in: Computer methods in applied mechanics and engineering Vol. 342; pp. 177 - 199
• Main Authors: Yang, Wen-Chia, Arduino, Pedro, Miller, Gregory R., Mackenzie-Helnwein, Peter
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.12.2018; Elsevier BV
• Subjects: Algorithms; Anti-locking and stabilization; Computational fluid dynamics; Destabilization; Energy dissipation; Error analysis; Fluid flow; Fluid mechanics; Fluid-structure interaction; Fluid–solid interaction; Flux; Incompressible flow; Material point method; Mathematical models; Meshfree methods; Numerical integration; Smoothing; Stabilization; Water flow; Material point method; Anti-locking and stabilization; Fluid–solid interaction; Meshfree methods
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2018.04.041

Phenomena involving general solid–water interactions such as flows with debris are challenging to model numerically because they are not easily represented using solid- or fluid-oriented methods. The material point method (MPM) provides a unified multi-material interaction platform potentially capable of modeling complex solid–water flow phenomena. However, it is necessary to address volumetric locking for (nearly) incompressible materials when modeling fluids, while also stabilizing integration errors that arise in standard MPM. This paper examines these challenges in depth, and presents a flux-based smoothing algorithm designed to address integration-error-induced destabilization via controlled strain energy dissipation. The effectiveness of the algorithm is demonstrated with two simple but fundamental fluid/solid problems, and with an application to a complex solid–water dynamic interaction problem. Results show the flux-based smoothing algorithm is capable of stabilizing the side-effects of numerical integration errors, while at the same time remaining inactive if there is no integration-error-induced oscillation. Based on this study, the flux-based smoothing algorithm is suggested as a stabilization scheme for MPM when using constant-interpolated hybrid elements. •This paper presents an approach for enabling MPM to be used for general fluid/solid interaction problems for which both anti-locking and stabilization are required to obtain suitable solutions.•To overcome shortcomings from prior formulations, this paper presents a flux-based algorithm which casts smoothing as a transport problem, and implements an energy dissipation control mechanism by means of controlling flux at cell interfaces.•The behavior of the newly proposed algorithm is demonstrated with basic smoothing examples, 1D and 2D validation examples and an application to a water–solid dynamic interaction problem.•Overall, the results presented in the paper demonstrate that the flux-based algorithm is able to stabilize a complex hydrodynamic analysis involving splashing fluid and complex fluid–solid interaction, and hence is a good candidate for handling tsunami–debris–structure interactions problems.