Three-dimensional unstructured grid Euler computations using a fully-implicit, upwind method

Whitaker, David L.

doi:10.2514/6.1993-3337

Cited by 25 publications

(4 citation statements)

References 7 publications

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“…The advection scheme that Premo currently uses is the approximate Riemann solver of Roe [183] with the entropy fix of Liou and van Leer [148] and the implementation closely follows that of Whitaker [216]. This schemes require a left (+) and right(-) state in order to evaluate the interface fluxes.…”

Section: Algorithmic Formulationmentioning

confidence: 99%

Sensitivity technologies for large scale simulation.

Collis¹,

Bartlett²,

Smith³

et al. 2005

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Section: Algorithmic Formulationmentioning

confidence: 99%

Sensitivity technologies for large scale simulation.

Collis¹,

Bartlett²,

Smith³

et al. 2005

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“…The use of GMRES combined with different preconditioning techniques is becoming widespread in the CFD community for the solution of the Euler and Navier-Stokes Eqs. [8,[20][21][22][23] GMRES minimizes the norm of the computed residual vector over the subspace spanned by a certain number of orthogonal search directions. It is well known that the speed of convergence of an iterative algorithm for a linear system depends on the condition number of the matrix A. GMRES works best when the eigenvalues of matrix A are clustered.…”

Section: Implicit Tlme Integrationmentioning

confidence: 99%

A Fast, Matrix-free Implicit Method for Computing Low Mach Number Flows on Unstructured Grids

Luo

Baum

Löhner

2000

International Journal of Computational Fluid Dynamics

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A fast, matrix-free implicit method has been developed to solve low Mach number flow problems on unstructured grids. The preconditioned compressible Euler and NavierStokes equations are integrated in time using a linearized implicit scheme. A newly developed fast, matrix-free implicit method, GMRES+ LU-SGS, is then applied to solve the resultant system of linear equations. A variety of computations has been made for a wide range of flow conditions, for both inviscid and viscous flows, in both 2D and 3D to validate the developed method and to evaluate the effectiveness of the GMRES + LU-SGS method. The numerical results obtained indicate that the use of the GM RES + LU-SGS method leads to a significant increase in performance over the LU-SGS method, while maintaining memory requirements similar to its explicit counterpart. An overall speedup factor from one to more than two order of magnitude for all test cases in comparison with the explicit method is demonstrated.

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“…Some of these factors are directly related to the maturity of several numerical aspects at the core of CFD. These include: multi-grid acceleration techniques [1][2][3][4] with enhanced equation solvers [5,6] that have decreased the computational cost of tackling large problems, better discretization techniques, unstructured grids [7][8][9][10][11][12], bounded high resolution schemes [13][14][15][16][17][18], as well as improved pressure-velocity (and density) coupling algorithms for fluid flow at all speeds [19][20][21][22][23][24][25][26][27]. Other factors, independent of the CFD industry, have to do with the exponential increase in processor power and decrease in microprocessor cost, whereby multiprocessors systems with large memory can now be set up at a fraction the cost of the super-computers of a decade ago.…”

Section: Introductionmentioning

confidence: 99%

The Geometric Conservation Based Algorithms For Multi-Fluid Flow At All Speeds

Moukalled¹

2002

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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the burden, to Department of Defense, Washington Headquarters Services, Directorate for Information PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)American University of Beirut ME Dept. PO Box: 11-0236 Beirut Lebanon PERFORMING ORGANIZATION REPORT NUMBERN/A SPONSOR/MONITOR'S ACRONYM(S) 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)EOARD PSC 802 BOX 14 FPO 09499-0014 SPONSOR/MONITOR'S REPORT NUMBER(S)SPC 01-4005 DISTRIBUTION/AVAILABILITY STATEMENTApproved for public release; distribution is unlimited. SUPPLEMENTARY NOTES ABSTRACTThis report results from a contract tasking American University of Beirut as follows: The proposed work involves implementing and (thoroughly) testing the Geometric Conservation Based family of Algorithms within a structured finite-volume framework. The convection terms along the control volume faces will be evaluated using a High Resolution scheme applied within the context of the Normalized Variable Formulation methodology. In order to accelerate the convergence rate and reduce the overall computational cost of the algorithm, the outer iterations will be accelerated by using a non-linear full multigrid method. The discretization scheme will be second-order accurate in space and first order accurate in time (even though extension to second order accuracy should be straightforward). The newly implemented algorithms will be tested by solving a variety of two-dimensional multi-fluid flow problems in the subsonic, transonic, and supersonic regimes. Examples include: 1) Phase separation in a duct (water-air); 2) Turbulent bubbly flow in a pipe; 3) Turbulent gas-solid flow in a curved duct; 4) Dusty flow over a flat plate at subsonic flow conditions (~incompressible); 5) Dusty flow in a converging-diverging nozzle, and 6) Any problem of interest to Dr. Sekar (AFRL/PR). A detailed report describing the work will be submitted at end of contract as specified in the schedule of supplies in the submitted proposal. SUBJECT TERMS AbstractThis work is concerned with the implementation and testing, within a structured collocated finite-volume framework, of seven segregated algorithms for the prediction of multi-phase flow at all speeds. These algorithms belong to the Geometric Conservation Based Algorithms

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Three-dimensional unstructured grid Euler computations using a fully-implicit, upwind method

Cited by 25 publications

References 7 publications

Sensitivity technologies for large scale simulation.

Sensitivity technologies for large scale simulation.

A Fast, Matrix-free Implicit Method for Computing Low Mach Number Flows on Unstructured Grids

The Geometric Conservation Based Algorithms For Multi-Fluid Flow At All Speeds

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