scholarly journals Strong and auxiliary forms of the semi-Lagrangian method for incompressible flows

2005 ◽  
Vol 25 (1-2) ◽  
pp. 323-346 ◽  
Author(s):  
D. Xiu ◽  
S. J. Sherwin ◽  
S. Dong ◽  
G. E. Karniadakis
Keyword(s):  
Incompressible Flows ◽  
Lagrangian Method

scholarly journals Boundary variation diminished conservative semi-Lagrangian method for both compressible and incompressible flows

2021 ◽  
Vol 33 (11) ◽  
pp. 117114
Author(s):  
Qijie Li ◽  
Junqiang Xia ◽  
Kensuke Yokoi ◽  
Syazana Omar
Keyword(s):  
Incompressible Flows ◽  
Lagrangian Method ◽  
Boundary Variation

scholarly journals Strong and Auxiliary Forms of the Semi-Lagrangian Method for Incompressible Flows

2005 ◽  
Vol 25 (1) ◽  
pp. 323-346 ◽  
Author(s):  
D. Xiu ◽  
S. J. Sherwin ◽  
S. Dong ◽  
G. E. Karniadakis
Keyword(s):  
Incompressible Flows ◽  
Lagrangian Method

SLAC – a semi-Lagrangian artificial compressibility solver for steady-state incompressible flows

2019 ◽  
Vol 29 (6) ◽  
pp. 1965-1983 ◽  
Author(s):  
Mohammad Mortezazadeh ◽  
Liangzhu (Leon) Wang
Keyword(s):  
Parallel Computing ◽  
Poisson Equation ◽  
Incompressible Flows ◽  
Gpu Computing ◽  
Lagrangian Method ◽  
Elliptic Type ◽  
Content Type ◽  
Artificial Compressibility ◽  
The Poisson Equation ◽  
Speed Up

Purpose The purpose of this paper is the development of a new density-based (DB) semi-Lagrangian method to speed up the conventional pressure-based (PB) semi-Lagrangian methods. Design/methodology/approach The semi-Lagrangian-based solvers are typically PB, i.e. semi-Lagrangian pressure-based (SLPB) solvers, where a Poisson equation is solved for obtaining the pressure field and ensuring a divergence-free flow field. As an elliptic-type equation, the Poisson equation often relies on an iterative solution, so it can create a challenge of parallel computing and a bottleneck of computing speed. This study proposes a new DB semi-Lagrangian method, i.e. the semi-Lagrangian artificial compressibility (SLAC), which replaces the Poisson equation by a hyperbolic continuity equation with an added artificial compressibility (AC) term, so a time-marching solution is possible. Without the Poisson equation, the proposed SLAC solver is faster, particularly for the cases with more computational cells, and better suited for parallel computing. Findings The study compares the accuracy and the computing speeds of both SLPB and SLAC solvers for the lid-driven cavity flow and the step-flow problems. It shows that the proposed SLAC solver is able to achieve the same results as the SLPB, whereas with a 3.03 times speed up before using the OpenMP parallelization and a 3.35 times speed up for the large grid number case (512 × 512) after the parallelization. The speed up can be improved further for larger cases because of increasing the condition number of the coefficient matrixes of the Poisson equation. Originality/value This paper proposes a method of avoiding solving the Poisson equation, a typical computing bottleneck for semi-Lagrangian-based fluid solvers by converting the conventional PB solver (SLPB) to the DB solver (SLAC) through the addition of the AC term. The method simplifies and facilitates the parallelization process of semi-Lagrangian-based fluid solvers for modern HPC infrastructures, such as OpenMP and GPU computing.

Finite Spectral Semi-Lagrangian Method for Incompressible Flows

2012 ◽  
Vol 29 (2) ◽  
pp. 024701
Author(s):  
Shao-Wu Li ◽  
Jian-Ping Wang
Keyword(s):  
Incompressible Flows ◽  
Lagrangian Method

Numerical solution of the reduced Navier-Stokes equations for internal incompressible flows

AIAA Journal ◽  
2000 ◽  
Vol 38 ◽  
pp. 1603-1614
Author(s):  
Martin Scholtysik ◽  
Bernhard Mueller ◽  
Torstein K. Fannelop
Keyword(s):  
Numerical Solution ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations

Momentum variable procedure for solving compressible and incompressible flows

AIAA Journal ◽  
1997 ◽  
Vol 35 ◽  
pp. 1801-1805
Author(s):  
M. Darbandi ◽  
G. E. Schneider
Keyword(s):  
Incompressible Flows ◽  
Momentum Variable
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