A Novel Staggered Semi-implicit Space-Time Discontinuous Galerkin Method for the Incompressible Navi

• 作 者: F.L.Romeo M.Dumbser M.Tavelli
• 机 构: Department of Civil,Environmental and Mechanical Engineering,University of Trento,Via Mesiano 77,381
• 出 处: 应用数学与计算数学学报
• 发表日期: 2021年4期
• 关键词: Incompressible Navier-Stokes equations Semi-implicit space-time discontinuous Ga

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 trian-gular grids in two space dimensions.The 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 mesh.In this paper,a new pair of equal-order-interpolation velocity-pressure finite elements is proposed.On the primary triangular mesh(the pressure elements),the basis func-tions are piecewise polynomials of degree N and are allowed to jump on the boundaries of each triangle.On 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 quad-rilateral and are allowed to jump only on the dual element boundaries,while they are continu-ous inside.In other words,the basis functions on the dual mesh are built by continuous finite elements on the subtriangles.This choice allows the construction of an efficient,quadrature-free and memory saving algorithm.In our coupled space-time pressure correction formulation for the incompressible Navier-Stokes equations,the arbitrary high order of accuracy in time is achieved through the use of time-dependent test and basis functions,in combination with sim-ple and efficient Picard iterations.Several 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.