Galerkin local maximum entropy method. (30th May 2018)

• Record Type: Journal Article
• Authors: Dreier, Nils‐Arne; Engwer, Christian; Hartmann, Dirk
• Is Part Of: International journal for numerical methods in fluids. Volume 88:Number 2(2018)
• Page Start: 100
• Page End: 115
• Publication Date: 2018-05-30
• Subjects: element‐free Galerkin method -- incompressible flow -- local maximum entropy approximation -- meshfree methods -- optimal transportation meshfree method; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4513
• Languages: English
• ISSNs: 0271-2091

Abstract

Summary: We propose a new particle‐based method for simulating incompressible Navier‐Stokes flows. It is based on a reinterpretation of the optimal transportation meshfree method within the context of Galerkin discretization. This enables us to introduce the incompressibility constraint into the formulation. Furthermore, we present convergence test and illustrate the usability of the method along several test problems. Abstract : Galerkin local maximum entropy method by Nils‐Arne Dreier*, Christian Engwer, Dirk Hartmann. We reinterpret the OTM by Li, Habbal, and Ortiz in the context of Galerkin discretization. This enables us to introduce constraints, like incompressibility, and stabilization terms. Ultimately, this allows the use of larger time steps and thus faster simulation. Furthermore, we provide results of numerical tests, which approve the robustness of the method.