Implicit Lower-Upper/Approximate-Factorization Schemes for Incompressible Flows

Briley, W. R.; Neerarambam, Shyam; Whitfield, David L.

doi:10.1006/jcph.1996.0194

Cited by 23 publications

(8 citation statements)

References 9 publications

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“…Introducing a parameter a when partitioning the coef cient matrix, as proposed by Whit eld, 9 it is possible to seek to improve the convergence rate by nding a value of a that minimizes the error introduced by the AF. This general formulation is indicated as the LU-AF scheme.…”

Section: Lu-af Factorizationmentioning

confidence: 99%

“…5 Yoon and Jameson,6,7 combined the LU factorization with a symmetric Gauss-Seidel (SGS) relaxation method to devise the more ef cient LU-SGS scheme and applied the scheme to transonic ows. For incompressible ows, Whit eld 8 and Briley et al 9 recently proposed a general LU-AF formulation that includes both the LU and LU-SGS schemes as particular cases, coupled with a Newton-Raphson procedure to reduce the factorization and linearization error.…”

Section: Introductionmentioning

confidence: 99%

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Factorized Implicit Upwind Methods Applied to Inviscid Flows at High Mach Number

2000

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The performance of several approximate factorization methods, coupled with a nite volume spatial discretization using Roe's approximate Riemann solver, are compared by means of numerical tests on a two-dimensional steady inviscid ow past a blunt body at Mach numbers ranging from 5 to 20. The comparisons are carried out evaluating, by numerical experiments, the optimal Courant number of each method. The alternating direction implicit and the lower-upper symmetric Gauss-Seidel methods result in the most ef cient factorizations, in terms of CPU time. The former behaves smoothly with increasing Mach number, and its performance is not affected by the grid size. The latter may achieve higher ef ciency but is strongly dependent on the number of relaxation steps performed, requiring optimization in terms of Mach number and grid size.

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Section: Lu-af Factorizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Factorized Implicit Upwind Methods Applied to Inviscid Flows at High Mach Number

2000

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“…To be parallel with compressible flow solvers, upwind characteristic-based schemes are frequently used. In this work, Roe's flux-splitting scheme is used in conjunction with Van Leer's MUSCL formulation, which was first applied to incompressible flows by Whitfield and co-workers [11,31]. Taking the ξ direction as an example, the inviscid derivative is discretized as…”

Section: Time and Spatial Discretizationsmentioning

confidence: 99%

“…The upwind differencing schemes that have been used include the flux-differencing splitting [9,10], MUSCL [11,12], TVD [13,14], and WENO [15] schemes; the solution techniques that have been implemented cover the BeamWarming scheme [16,17], the approximation factorization-planar symmetric Gauss-Seidel scheme [13], lower-upper symmetric Gauss-Seidel (LU-SGS) scheme [15,18], line and point relaxation schemes [10,19], the explicit multistage Runge-Kutta method [20], and so on. The application is also extended to unsteady flow computations [9,10,20] by using a dual-time-stepping procedure that subiterates at each physical time step and drives the divergence of the velocity toward zero.…”

Section: Introductionmentioning

confidence: 99%

“…The author also tried the LU-SGS scheme [18,38] and the approximation factorization-planar symmetric Gauss-Seidel scheme [13] and found that the overall computing time was greater than that of the diagonalized ADI scheme; thus these implicit schemes were excluded in this work. The discretization for the convective terms used is an upwind differencing scheme based on Roe's approximate Riemann solver [39] with Van Leer's MUSCL formulation [40], which was applied to the ACM and recommended for its computational efficiency and accuracy in [11,31]. The MUSCL formulation was usually used together with limiters, but it was found that they are not necessary for the present cases.…”

Section: Introductionmentioning

confidence: 99%

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Comparison of Implicit Multigrid Schemes for Three-Dimensional Incompressible Flows

2002

Journal of Computational Physics

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To develop a robust and efficient computational flow simulation tool for incompressible flow applications, a number of different implicit multigrid schemes for solving the three-dimensional incompressible Navier-Stokes equations are compared in the current study. These schemes consist of a common full approximation storage (FAS) multigrid algorithm implemented in conjunction with three different implicit schemes, which include a modified point Gauss relaxation, a standard Gauss-Seidel line relaxation, and the Beam-Warming alternating direction implicit (ADI) scheme. The flow solver used in the study is based on artificial compressibility and uses a third-order upwind difference for the convective terms and a second-order central difference for the viscous terms. The efficiency of each implicit multigrid scheme is assessed in terms of the computing time required for two laminar flow problems: the entry flow through a 90• bent square duct, and the steady-state and unsteady flows past a prolate spheroid at incidence with an axis ratio of 4 : 1. It is found that implementation of Neumann boundary conditions on the coarse grid in terms of the flow variable correction rather than the flow variable itself is essential for obtaining good convergence in the collocated finite difference discretization. The results of steady-state flow computations show that all the implicit multigrid schemes yield more than 50% computational time savings over their single grid counterparts, and the point or line relaxation multigrid scheme outperforms the ADI multigrid scheme by at least a factor of 2. However, in unsteady flow computations, the computational time saving of the multigrid scheme is less than that in steady-state cases. The current study concludes that the FAS multigrid algorithm implemented with the modified point Gauss relaxation scheme is preferable for simulating both steady-state and time-dependent incompressible flows. c 2002 Elsevier Science (USA)

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Finite element solution of free-surface ship-wave problems

Idelsohn

Oñate

Sacco

1999

Int. J. Numer. Meth. Engng.

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SUMMARYAn unstructured ÿnite element solver to evaluate the ship-wave problem is presented. The scheme uses a non-structured ÿnite element algorithm for the Euler or Navier-Stokes ow as for the free-surface boundary problem. The incompressible ow equations are solved via a fractional step method whereas the non-linear free-surface equation is solved via a reference surface which allows ÿxed and moving meshes. A new nonstructured stabilized approximation is used to eliminate spurious numerical oscillations of the free surface.

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Implicit Lower-Upper/Approximate-Factorization Schemes for Incompressible Flows

Cited by 23 publications

References 9 publications

Factorized Implicit Upwind Methods Applied to Inviscid Flows at High Mach Number

Factorized Implicit Upwind Methods Applied to Inviscid Flows at High Mach Number

Comparison of Implicit Multigrid Schemes for Three-Dimensional Incompressible Flows

Finite element solution of free-surface ship-wave problems

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