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Preconditioned methods for solving the incompressible and low speed compressible equations. (English) Zbl 0633.76069
Acceleration methods are presented for solving the steady state incompressible equations. These systems are preconditioned by introducing artificial time derivatives which allow for a faster convergence to the steady state. We also consider the compressible equations in conservation form with slow flow. Two arbitrary functions \(\alpha\) and \(\beta\) are introduced in the general preconditioning. An analysis of this system is presented and an optimal value for \(\beta\) is determined given a constant \(\alpha\). It is further shown that the resultant incompressible equations form a symmetric hyperbolic system and so are well posed. Several generalizations to the compressible equations are presented which extend previous results.

MSC:
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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[1] Beam, R.M.; Warming, R.F., J. comput. phys., 22, 87, (1976)
[2] Bailey, W.R.; Mcdonald, H.; Shamroth, S.J., Aiaa j., 21, 1467, (1983)
[3] Chang, J.L.C.; Kwak, D., AIAA paper 84-0252, (1984), (unpublished)
[4] Choi, D.; Merkle, C.L., Aiaa j., 23, 1518, (1985)
[5] Choi, D.; Merkle, C.L., AIAA paper 86-0351, (1986), (unpublished)
[6] Chorin, A.J., J. comput. phys., 2, 12, (1967)
[7] Gottlieb, D.; Gustaffson, B., Stud. appl. math., 11, 167, (1976)
[8] Jameson, A.; Turkel, E., Math. comput., 37, 385, (1981)
[9] Jameson, A.; Schmidt, W.; Turkel, E., AIAA paper 81-1259, (1981), (unpublished)
[10] Peyret, R.; Taylor, T., Computational methods for fluid flow, (1983), Springer New York · Zbl 0514.76001
[11] Pulliam, T.H.; Steger, J.L., AIAA paper 85-0360, (1985), (unpublished)
[12] Rizzi, A.; Eriksson, L.E., J. fluid mech., 153, 275, (1985)
[13] Rizzi, A., Hyperbolic preconditioning to solve the incompressible Euler equations for vortex flow, () · Zbl 0606.76028
[14] Rogers, S.E.; Kwak, D.; Kaul, U., AIAA paper 85-1689, (1985), (unpublished)
[15] Sox, W.Y.; Berger, S.A., J. fluid mech., 48, 109, (1984)
[16] Steger, J.L.; Kutler, P., Aiaa j., 15, 581, (1977)
[17] Turkel, E., (), 571
[18] Turkel, E., (), 281
[19] Turkel, E., (), 155
[20] Viviano, H., ONERA publication 69, (1984), (unpublished)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.