AN EXPONENTIAL TIME INTEGRATOR FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATION

被引：5

作者：

Kooij, Gijs L. ^{[1
]}

Botchev, Mike A. ^{[2
,3
]}

Geurts, Bernard J. ^{[1
,4
]}

机构：

[1] Univ Twente, Fac EEMCS, Multiscale Modeling & Simulat, Enschede, Netherlands

[2] Univ Twente, Fac EEMCS, Math Computat Sci, Enschede, Netherlands

[3] Russian Acad Sci, Keldysh Inst Appl Math, Moscow, Russia

[4] Eindhoven Univ Technol, Fac Appl Phys, Fluid Dynam Lab, Eindhoven, Netherlands

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2018年 / 40卷 / 03期

基金：

俄罗斯科学基金会;

关键词：

exponential time integration; incompressible Navier-Stokes equation; block Krylov subspace method; parallel in time; INITIAL-VALUE PROBLEMS; RUNGE-KUTTA METHODS; NUMERICAL-SOLUTION; KRYLOV SUBSPACES; FLOW; MATRIX; PARAREAL; APPROXIMATION; SYSTEMS; IMPLEMENTATION;

D O I：

10.1137/17M1121950

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present an exponential time integration method for the incompressible Navier-Stokes equation. An essential step in our procedure is the treatment of the pressure by applying a divergence-free projection to the momentum equation. The differential-algebraic equation for the discrete velocity and pressure is then reduced to a conventional ordinary differential equation that can be solved with the proposed exponential integrator. A promising feature of exponential time integration is its potential time parallelism within the Paraexp algorithm. We demonstrate that our approach leads to parallel speedup assuming negligible parallel communication.

引用

页码：B684 / +

页数：23

共 66 条

[1]

[Anonymous], 2014, FINITE ELEMENTS FAST, DOI DOI 10.1093/ACPROF:OSO/9780199678792.003.0009

[2]

[Anonymous], 2003, ITERATIVE METHODS SP, DOI DOI 10.1137/1.9780898718003

[3]

Benzi M, 2005, ACTA NUMER, V14, P1, DOI 10.1017/S0962492904000212

[4] A parallel implementation of the modified augmented Lagrangian preconditioner for the incompressible Navier-Stokes equations [J].

Benzi, Michele ;

Wang, Zhen .

NUMERICAL ALGORITHMS, 2013, 64 (01) :73-84

[5] GENERALIZED RATIONAL KRYLOV DECOMPOSITIONS WITH AN APPLICATION TO RATIONAL APPROXIMATION [J].

Berljafa, Mario ;

Guettel, Stefan .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2015, 36 (02) :894-916

[6] A block Krylov subspace time-exact solution method for linear ordinary differential equation systems [J].

Botchev, M. A. .

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2013, 20 (04) :557-574

[7] RESIDUAL, RESTARTING, AND RICHARDSON ITERATION FOR THE MATRIX EXPONENTIAL [J].

Botchev, Mike A. ;

Grimm, Volker ;

Hochbruck, Marlis .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2013, 35 (03) :A1376-A1397

[8] Benchmark spectral results on the lid-driven cavity flow [J].

Botella, O ;

Peyret, R .

COMPUTERS & FLUIDS, 1998, 27 (04) :421-433

[9] The 2D lid-driven cavity problem revisited [J].

Bruneau, CH ;

Saad, M .

COMPUTERS & FLUIDS, 2006, 35 (03) :326-348

[10]

Burrage K., 1995, Parallel and Sequential Methods for Ordinary Differential Equations

← 1 2 3 4 5 6 7 →