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A Novel staggered Semi-implicit Space-Time Discontinuous Galerkin Method for the Incompressible Navier-Stokes Equations

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Communications on Applied Mathematics and Computation 2021年第4期3卷 607-647页

作者： F.L.Romeo M.Dumbser M.Tavelli Department of Civil Environmental and Mechanical EngineeringUniversity of TrentoVia Mesiano 7738123 TrentoItaly

A new high-order accurate staggered semi-implicit space-time discontinuous Galerkin(DG)method is presented for the simulation of viscous incompressible flows on unstructured triangular grids in two space *** staggered DG scheme defines the discrete pressure on the primal triangular mesh,while the discrete velocity is defined on a staggered edge-based dual quadrilateral *** this paper,a new pair of equal-order-interpolation velocity-pressure finite elements is *** the primary triangular mesh(the pressure elements),the basis functions are piecewise polynomials of degree N and are allowed to jump on the boundaries of each *** the dual mesh instead(the velocity elements),the basis functions consist in the union of piecewise polynomials of degree N on the two subtriangles that compose each quadrilateral and are allowed to jump only on the dual element boundaries,while they are continuous *** other words,the basis functions on the dual mesh arc built by continuous finite elements on the *** choice allows the construction of an efficient,quadrature-free and memory saving *** our coupled space-time pressure correction formulation for the incompressible Navier-Stokes equations,the arbitrary high order of accuracy in time is achieved through tire use of time-dependent test and basis functions,in combination with simple and efficient Picard *** numerical tests on classical benchmarks confirm that the proposed method outperforms existing staggered semi-implicit space-time DG schemes,not only from a computer memory point of view,but also concerning the computational time.

关键词： Incompressible Navier-Stokes equations Semi-implicit space-time discontinuous Galerkin schemes staggered unstructured meshes Space-time pressure correction method High-order accuracy in space and time

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