Print Email Facebook Twitter A hybridized discontinuous Galerkin framework for high-order particle–mesh operator splitting of the incompressible Navier–Stokes equations Title A hybridized discontinuous Galerkin framework for high-order particle–mesh operator splitting of the incompressible Navier–Stokes equations Author Maljaars, J.M. (TU Delft Environmental Fluid Mechanics; TU Delft Rivers, Ports, Waterways and Dredging Engineering) Labeur, R.J. (TU Delft Environmental Fluid Mechanics) Möller, M. (TU Delft Numerical Analysis) Date 2018-04-01 Abstract A generic particle–mesh method using a hybridized discontinuous Galerkin (HDG) framework is presented and validated for the solution of the incompressible Navier–Stokes equations. Building upon particle-in-cell concepts, the method is formulated in terms of an operator splitting technique in which Lagrangian particles are used to discretize an advection operator, and an Eulerian mesh-based HDG method is employed for the constitutive modeling to account for the inter-particle interactions. Key to the method is the variational framework provided by the HDG method. This allows to formulate the projections between the Lagrangian particle space and the Eulerian finite element space in terms of local (i.e. cellwise) ℓ2-projections efficiently. Furthermore, exploiting the HDG framework for solving the constitutive equations results in velocity fields which excellently approach the incompressibility constraint in a local sense. By advecting the particles through these velocity fields, the particle distribution remains uniform over time, obviating the need for additional quality control. The presented methodology allows for a straightforward extension to arbitrary-order spatial accuracy on general meshes. A range of numerical examples shows that optimal convergence rates are obtained in space and, given the particular time stepping strategy, second-order accuracy is obtained in time. The model capabilities are further demonstrated by presenting results for the flow over a backward facing step and for the flow around a cylinder. Subject Finite elementsHybridized discontinuous GalerkinIncompressible Navier–Stokes equationsLagrangian–EulerianMaterial point methodParticle-in-cell To reference this document use: http://resolver.tudelft.nl/uuid:d5cd841b-51f9-4088-9de0-312d066c1902 DOI https://doi.org/10.1016/j.jcp.2017.12.036 Embargo date 2020-01-10 ISSN 0021-9991 Source Journal of Computational Physics, 358, 150-172 Part of collection Institutional Repository Document type journal article Rights © 2018 J.M. Maljaars, R.J. Labeur, M. Möller Files PDF JCP_Maljaarsetal_20181117.pdf 2.09 MB Close viewer /islandora/object/uuid:d5cd841b-51f9-4088-9de0-312d066c1902/datastream/OBJ/view