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M.-S. Liou, and B. Van Leer, Choice of Implicit and Explicit Operators for the Upwind Differencing Method, AIAA Paper, AIAA-88-0624 (1988).

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Krylov Methods for Compressible Flows - Tidriri (1995)   (3 citations)  (Correct)

....operators together with explicit treatment of the boundary conditions, lead to severely limited CFL number, which results in a slow convergence to steady state aerodynamic solutions. Many authors have tried to replace explicit boundary conditions with implicit ones (see for instance [19] 15] and [8]) They showed that high CFL number can be used, however no clear advantages in terms of CPU time as compared to explicit boundary conditions have been drawn. We investigate here defect correction procedures based on Krylov methods; more particularly we study the ILU GMRES methods together with ....

M.-S. Liou, and B. Van Leer, Choice of Implicit and Explicit Operators for the Upwind Differencing Method, AIAA Paper, AIAA-88-0624 (1988).


Finite Elements For Cfd - How Does The Theory Compare? - Baker, Chaffin, Iannelli, Roy   (Correct)

.... on c for a monotone solution [22] which is specifically solution dependent for the non linear problem (1) Performance of the SGM element is confirmed for numerous verifications and benchmarks for n=1, 2, 3 [21,22] Of particular note is the off design de Laval nozzle shock benchmark problem [23], containing numerous subtle features. Figure 5 summarizes the essence of the comparative steady solutions obtained via TWS and SGM methodologies. The TWS solutions are monotone only for the shock smeared across three or more elements. Conversely, the SGM Figure 4. GWS TWS k=1 algorithm ....

M.S. Liou and B. van Leer, `Choice of implicit and explicit operators for the upwind differencing method', Tech. AIAA 88-0624, 26th Aerospace Sciences Meeting, 1988.


A New Monotone Time Relaxation Matrix Procedure For Improved .. - Subrata Roy Baker   (Correct)

....cross sectional area distribution. For a perfect gas, 47a b) is closed by the polytropic equation of state (47d) and for velocity u = m=ae, the volume specific total energy E is E = p fl Gamma 1 1 2 aeu 2 (48) The de Laval nozzle geometry, Figure 4, and test problem specification of [11] is used for the verification test with A(x) 1:75 Gamma 0:75 cos[2(x Gamma 0:5) 0:0 x 0:5 1:25 Gamma 0:25 cos[2(x Gamma 0:5) 0:5 x 1:0 (49) The non dimensional initial condition for q is derived from the sonic, shock free isentropic solution for (49) The boundary conditions ....

M.S. Liou and B. van Lerr, Choice of implicit and explicit operators for the upwind differencing method, Tech. Paper AIAA 88-0624 (26th Aerospace Meeting, Reno, Nevada, 1988)


Schwarz-based algorithms for compressible flows - Tidriri (1996)   (2 citations)  (Correct)

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M.-S. Liou, and B. Van Leer, Choice of Implicit and Explicit Operators for the Upwind Differencing Method, AIAA Paper, AIAA-88-0624 (1988).

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