A diagonalized diagonal dominant alternating direction implicit (D3ADI) scheme and subiteration correction

Klopfer, G. H.; Hung, Ching Mao; Wijngaart, Rob Van der; Onufer, Jeff T.

doi:10.2514/6.1998-2824

Cited by 41 publications

(19 citation statements)

References 8 publications

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“…ARC2D uses a generalized curvilinear coordinate system and the diagonal form [20] of the Beam-Warming approximate factorization algorithm [4] with local time stepping to solve the thin-layer Navier-Stokes equations. With the upwind-biased spatial discretization, convergence to steady state is achieved using the diagonally dominant approximate factorization algorithm in diagonal form of Klopfer et al [14] with three subiterations per time step. The effects of turbulence are modelled using the Baldwin-Lomax model [2], and a far-field circulation correction is included at the outer boundary [19].…”

Section: Governing Equations and Numerical Methodsmentioning

confidence: 99%

Comparison of several spatial discretizations for the Navier-Stokes equations

Zingg¹,

Rango²,

Nemec³

et al. 1999

14th Computational Fluid Dynamics Conference

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Grid convergence studies for subsonic and transonic flows over airfoils are presented in order to compare the accuracy of several spatial discretizations for the compressible Navier-Stokes equations. The discretizations include the following schemes for the inviscid fluxes: (1) second-order-accurate centered differences with third-order matrix numerical dissipation, (2) the second-order convective upstream split pressure scheme (CUSP), (3) third-order upwind-biased differencing with Roe's flux-difference splitting, and (4) fourth-order centered differences with third-order matrix numerical dissipation. The first three are combined with second-order differencing for the grid metrics and viscous terms. The fourth discretization uses fourthorder differencing for the grid metrics and viscous terms, as well as higher-order approximations near boundaries and for the numerical integration used to calculate forces and moments. The results indicate that the discretization using higher-order approximations for all terms is substantially more accurate than the others, producing less than two percent numerical error in lift and drag components on grids with less than 13,000 nodes for subsonic cases and less than 18,000 nodes for transonic cases. Since the cost per grid node of all of the discretizations studied is comparable, the higher-order discretization produces solutions of a given accuracy much more efficiently than the others.

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Section: Governing Equations and Numerical Methodsmentioning

confidence: 99%

Comparison of several spatial discretizations for the Navier-Stokes equations

Zingg¹,

Rango²,

Nemec³

et al. 1999

14th Computational Fluid Dynamics Conference

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“…An implicit DDADI algorithm [7] is used to discretize the remaining time derivative in Equation (2.2). Deÿne a residual as…”

Section: Time Integrations: Ddadi Algorithm and Crank-nicolson Methodsmentioning

confidence: 99%

“…Since the equations are hyperbolic dominated, some of the upwind ÿnite-volume schemes which have recently been developed for the compressible Euler and Navier-Stokes equations can be utilized. For the time integration, the second-order Crank-Nicolson method coupled with a DDADI time integration [7] is used. In the following sections, the details of the artiÿcial compressibility method and its applications in solving the incompressible Navier-Stokes equation for both steady-state and unsteady problems are given.…”

Section: Introductionmentioning

confidence: 99%

Vortex structure and strength of secondary flows in model aortic arches

Lin

2002

Numerical Methods in Fluids

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SUMMARYA numerical method is developed to study the ow structures in the aortic arch. The method solves the incompressible Navier-Stokes equations. It uses a third-order upwind scheme for the convective terms and the second-order central scheme for the viscous terms. A DDADI time integration is used for achieving fast convergence. For the unsteady solutions, the second-order Crank-Nicolson method coupled with the diagonalized diagonal dominated alternating direction implicit scheme (DDADI) time integration are used. The numerical results show that the method is about 2.5-order accuracy in space and 1.8-order accuracy in time. Then the method is used to investigate the vortex structure and strength of secondary ows in the aortic arch. Four di erent arch geometries are constructed to see the e ect of arch conÿguration. Many ow properties such as pressure drop, vortex strength and separation are computed and compared among the four arch models.

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“…51 and Ref. 52 and is used here as well. Note that the diagonal term M contains the diagonal contributions of E Q , F Q , F Q as well as S Q and is shared by both factors.…”

Section: Elliptic Solution Proceduresmentioning

confidence: 99%

A pseudo-temporal multi-grid relaxation scheme for solving the parabolized Navier-Stokes equations

White

Morrison

1999

14th Computational Fluid Dynamics Conference

131

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A m ulti-grid, ux-di erence-split, nite-volume code, VULCAN, is presented for solving the elliptic and parabolized form of the equations governing three-dimensional, turbulent, calorically perfect and non-equilibrium chemically reacting ows. The space marching algorithms developed to improve convergence rate and or reduce computational cost are emphasized. The algorithms presented are extensions to the class of implicit pseudo-time iterative, upwind space-marching schemes. A full approximate storage, full multi-grid scheme is also described which is used to accelerate the convergence of a Gauss-Seidel relaxation method. The multi-grid algorithm is shown to signi cantly improve convergence on high aspect ratio grids.

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A diagonalized diagonal dominant alternating direction implicit (D3ADI) scheme and subiteration correction

Cited by 41 publications

References 8 publications

Comparison of several spatial discretizations for the Navier-Stokes equations

Comparison of several spatial discretizations for the Navier-Stokes equations

Vortex structure and strength of secondary flows in model aortic arches

A pseudo-temporal multi-grid relaxation scheme for solving the parabolized Navier-Stokes equations

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