THE DEVELOPMENT OF A ONE‐STEP ACCURATE FLUX VECTOR‐SPLITTING IMPLICIT ALGORITHM FOR EULER AND NAVIER‐STOKES EQUATIONS

1996 ◽  
Vol 6 (8) ◽  
pp. 3-18
Author(s):  
E.Y.K. NG ◽  
S.Z. LIU
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Flux Vector ◽  
Navier Stokes Equations ◽  
Implicit Algorithm ◽  
Flux Vector Splitting ◽  
One Step

scholarly journals An implicit algorithm of solving Navier–Stokes equations to simulate flows in anisotropic porous media

2018 ◽  
Vol 160 ◽  
pp. 164-174
Author(s):  
A.S. Kozelkov ◽  
S.V. Lashkin ◽  
V.R. Efremov ◽  
K.N. Volkov ◽  
Yu. A. Tsibereva ◽  
...  
Keyword(s):  
Porous Media ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Anisotropic Porous Media ◽  
Navier Stokes Equations ◽  
Implicit Algorithm

An Implicit Algorithm for High-Order DG/FV Schemes for Compressible Flows on 2D Arbitrary Grids

2014 ◽  
Vol 17 (1) ◽  
pp. 287-316 ◽  
Author(s):  
Laiping Zhang ◽  
Ming Li ◽  
Wei Liu ◽  
Xin He
Keyword(s):  
Compressible Flows ◽  
Stokes Equations ◽  
Inviscid Flow ◽  
Implicit Scheme ◽  
Navier Stokes ◽  
Test Cases ◽  
Navier Stokes Equations ◽  
Hybrid Schemes ◽  
Implicit Algorithm ◽  
Update Frequency

AbstractA Newton/LU-SGS (lower-upper symmetric Gauss-Seidel) iteration implicit method was developed to solve two-dimensional Euler and Navier-Stokes equations by the DG/FV hybrid schemes on arbitrary grids. The Newton iteration was employed to solve the nonlinear system, while the linear system was solved with LU-SGS iteration. The effect of several parameters in the implicit scheme, such as the CFL number, the Newton sub-iteration steps, and the update frequency of Jacobian matrix, was investigated to evaluate the performance of convergence history. Several typical test cases were simulated, and compared with the traditional explicit Runge-Kutta (RK) scheme. Firstly the Couette flow was tested to validate the order of accuracy of the present DG/FV hybrid schemes. Then a subsonic inviscid flow over a bump in a channel was simulated and the effect of parameters was investigated also. Finally, the implicit algorithm was applied to simulate a subsonic inviscid flow over a circular cylinder and the viscous flow in a square cavity. The numerical results demonstrated that the present implicit scheme can accelerate the convergence history efficiently. Choosing proper parameters would improve the efficiency of the implicit scheme. Moreover, in the same framework, the DG/FV hybrid schemes are more efficient than the same order DG schemes.

Segmented Domain Decomposition Multigrid Solutions for Two and Three-Dimensional Viscous Flows

1993 ◽  
Vol 115 (4) ◽  
pp. 608-613
Author(s):  
Kumar Srinivasan ◽  
Stanley G. Rubin
Keyword(s):  
Domain Decomposition ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Flow ◽  
Mass Conservation ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Recirculation ◽  
Flux Vector Splitting

Several viscous incompressible two and three-dimensional flows with strong inviscid interaction and/or axial flow reversal are considered with a segmented domain decomposition multigrid (SDDMG) procedure. Specific examples include the laminar flow recirculation in a trough geometry and in a three-dimensional step channel. For the latter case, there are multiple and three-dimensional recirculation zones. A pressure-based form of flux-vector splitting is applied to the Navier-Stokes equations, which are represented by an implicit, lowest-order reduced Navier-Stokes (RNS) system and a purely diffusive, higher-order, deferred-corrector. A trapezoidal or box-like form of discretization insures that all mass conservation properties are satisfied at interfacial and outflow boundaries, even for this primitive-variable non-staggered grid formulation. The segmented domain strategy is adapted herein for three-dimensional flows and is extended to allow for disjoint subdomains that do not share a common boundary.

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