TY - JOUR

T1 - An iteration free backward semi-Lagrangian scheme for solving incompressible Navier-Stokes equations

AU - Piao, Xiangfan

AU - Bu, Sunyoung

AU - Bak, Soyoon

AU - Kim, Philsu

N1 - Publisher Copyright:
© 2014 Elsevier Inc.

PY - 2015/2/5

Y1 - 2015/2/5

N2 - A backward semi-Lagrangian method based on the error correction method is designed to solve incompressible Navier-Stokes equations. The time derivative of the Stokes equation is discretized with the second order backward differentiation formula. For the induced steady Stokes equation, a projection method is used to split it into velocity and pressure. Fourth-order finite differences for partial derivatives are used to the boundary value problems for the velocity and the pressure. Also, finite linear systems for Poisson equations and Helmholtz equations are solved with a matrix-diagonalization technique. For characteristic curves satisfying highly nonlinear self-consistent initial value problems, the departure points are solved with an error correction strategy having a temporal convergence of order two. The constructed algorithm turns out to be completely iteration free. In particular, the suggested algorithm possesses a good behavior of the total energy conservation compared to existing methods. To assess the effectiveness of the method, two-dimensional lid-driven cavity problems with large different Reynolds numbers are solved. The doubly periodic shear layer flows are also used to assess the efficiency of the algorithm.

AB - A backward semi-Lagrangian method based on the error correction method is designed to solve incompressible Navier-Stokes equations. The time derivative of the Stokes equation is discretized with the second order backward differentiation formula. For the induced steady Stokes equation, a projection method is used to split it into velocity and pressure. Fourth-order finite differences for partial derivatives are used to the boundary value problems for the velocity and the pressure. Also, finite linear systems for Poisson equations and Helmholtz equations are solved with a matrix-diagonalization technique. For characteristic curves satisfying highly nonlinear self-consistent initial value problems, the departure points are solved with an error correction strategy having a temporal convergence of order two. The constructed algorithm turns out to be completely iteration free. In particular, the suggested algorithm possesses a good behavior of the total energy conservation compared to existing methods. To assess the effectiveness of the method, two-dimensional lid-driven cavity problems with large different Reynolds numbers are solved. The doubly periodic shear layer flows are also used to assess the efficiency of the algorithm.

KW - Error correction method

KW - Fourth-order finite difference method

KW - Navier-Stokes equations

KW - Projection method

KW - Semi-Lagrangian method

UR - http://www.scopus.com/inward/record.url?scp=84918838823&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2014.11.040

DO - 10.1016/j.jcp.2014.11.040

M3 - Article

AN - SCOPUS:84918838823

SN - 0021-9991

VL - 283

SP - 189

EP - 204

JO - Journal of Computational Physics

JF - Journal of Computational Physics

ER -