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Comput. Phys.</a> <a href="/?q=in%3A52965" title="Articles in this Issue">140, No. 2, 311-345 (1998)</a>. </div> <div class="abstract">We compare currently used preconditioned Krylov subspace methods for inviscid and viscous flow engineering problems. The design of an implicit finite volume approximation of the Navier-Stokes equations on unstructured grids is described, whereby a new combination of isotropic triangulation with anisotropic subgrids is presented to achieve high resolution for high Reynolds number flows. Based on a specific selection of different inviscid and viscous flow fields, we discuss the choice of iterative method depending on the flow field for Euler and Navier-Stokes equations to get a stable and fast numerical scheme. \(\copyright\) Academic Press.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A1283483">Cited in <strong>10</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A76M12" title="MSC2020">76M12</a> </td> <td class="space"> Finite volume methods applied to problems in fluid mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A76N15" title="MSC2020">76N15</a> </td> <td class="space"> Gas dynamics (general theory) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65F10" title="MSC2020">65F10</a> </td> <td class="space"> Iterative numerical methods for linear systems </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Apreconditioned+Krylov+subspace+methods">preconditioned Krylov subspace methods</a>; <a href="/?q=ut%3Aimplicit+finite+volume+approximation">implicit finite volume approximation</a>; <a href="/?q=ut%3ANavier-Stokes+equations">Navier-Stokes equations</a>; <a href="/?q=ut%3Aunstructured+grids">unstructured grids</a>; <a href="/?q=ut%3Aisotropic+triangulation">isotropic triangulation</a>; <a href="/?q=ut%3Aanisotropic+subgrids">anisotropic subgrids</a></div> <div class="software"> <h3>Software:</h3><a href="/software/8225">CGS</a>; <a href="/software/2139">GMBACK</a></div> <!-- Modal used to show zbmath metadata in different output formats--> <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;"> <!-- alert for connection errors etc --> </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function"> <!-- Button trigger metadata modal --> <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 0935.76051" data-ciurl="/ci/01283483" data-biburl="/bibtex/01283483.bib" data-amsurl="/amsrefs/01283483.bib" data-xmlurl="/xml/01283483.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/01283483.pdf" title="Zbl 0935.76051 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1006/jcph.1998.5862" aria-label="DOI for “Comparison of different Krylov subspace methods embedded in an implicit finite volume scheme for the computation of viscous and inviscid flow fields on unstructured grids”" title="10.1006/jcph.1998.5862">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Ajmani, K.; Ng, W.-F.; Liou, M., Preconditioned conjugate gradient methods for the Navier-Stokes equations, J. Comput. Phys., 110, 68 (1994) · <a href="/0797.76065" class="nowrap">Zbl 0797.76065</a></td> </tr><tr> <td>[2]</td> <td class="space">Arnone, A.; Liou, M.-S.; Povinelli, L. A., Integration of Navier-Stokes equations using dual time stepping and a multigrid, AIAA J., 33, 985 (1995) · <a href="/0844.76069" class="nowrap">Zbl 0844.76069</a></td> </tr><tr> <td>[3]</td> <td class="space">Bank, R. E.; Chan, T. F., An analysis of the composite step biconjugate gradient method, Numer. Math., 66, 295 (1993) · <a href="/0802.65038" class="nowrap">Zbl 0802.65038</a></td> </tr><tr> <td>[4]</td> <td class="space">Barrett, R.; Berry, M.; Chan, T.; Demmel, J.; Donato, J.; Dongarra, J.; Eijkhout, V.; Pozo, R.; Romine, C.; van der Vorst, H., Templates for the Solution of Linear Systems (1994)</td> </tr><tr> <td>[5]</td> <td class="space">Barth, T. J.; Jesperson, D. C., The design and application of upwind schemes on unstructured meshes, AIAA Paper (1989)</td> </tr><tr> <td>[6]</td> <td class="space">Bramble, J. H.; Pasciak, J. E.; Schatz, A. H., The construction of preconditioners for elliptic problems by substructuring I, Math. Comp., 47, 103 (1986) · <a href="/0615.65112" class="nowrap">Zbl 0615.65112</a></td> </tr><tr> <td>[7]</td> <td class="space">Bramble, J. H.; Pasciak, J. E.; Schatz, A. H., The construction of preconditioners for elliptic problems by substructuring II, Math. Comp., 49, 1 (1987) · <a href="/0623.65118" class="nowrap">Zbl 0623.65118</a></td> </tr><tr> <td>[8]</td> <td class="space">Bramble, J. H.; Pasciak, J. E.; Schatz, A. H., The construction of preconditioners for elliptic problems by substructuring III, Math. Comp., 51, 415 (1988) · <a href="/0701.65070" class="nowrap">Zbl 0701.65070</a></td> </tr><tr> <td>[9]</td> <td class="space">Bramble, J. H.; Pasciak, J. E.; Schatz, A. H., The construction of preconditioners for elliptic problems by substructuring IV, Math. Comp., 53, 1 (1989) · <a href="/0623.65118" class="nowrap">Zbl 0623.65118</a></td> </tr><tr> <td>[10]</td> <td class="space">Brandt, A., Guide to multigrid development, Multigrid Methods, 960, 220 (1981) · <a href="/0505.65037" class="nowrap">Zbl 0505.65037</a></td> </tr><tr> <td>[11]</td> <td class="space">Brown, P. N., A theoretical comparison of the Arnoldi and GMRES algorithms, SIAM J. Sci. Stat. Comp., 12, 58 (1991) · <a href="/0719.65022" class="nowrap">Zbl 0719.65022</a></td> </tr><tr> <td>[12]</td> <td class="space">Cai, X.; Keyes, D. E.; Venkatakrishnan, V., Newton-Krylov-Schwarz: An Implicit Solver for CFD (1995)</td> </tr><tr> <td>[13]</td> <td class="space">Chan, T. F.; Gallopoulos, E.; Simoncini, V.; Szeto, T.; Tong, C. H., A quasi-minimal residual variant of the bi-cgstab algorithm for nonsymmetric systems, SIAM J. Sci. Comput., 15, 338 (1994) · <a href="/0803.65038" class="nowrap">Zbl 0803.65038</a></td> </tr><tr> <td>[14]</td> <td class="space">Courant, R.; Friedrichs, K. O.; Lewy, H., Uber die partiellen Differentialgleichungen der mathematischen Physik, Math. Ann., 100, 32 (1928) · <a href="/54.0486.01" class="nowrap">JFM 54.0486.01</a></td> </tr><tr> <td>[15]</td> <td class="space">Dervieux, A.; van Leer, B.; Periaux, J.; Rizzi, A., Numerical Simulation of Compressible Euler Flows, 26 (1989) · <a href="/0696.76004" class="nowrap">Zbl 0696.76004</a></td> </tr><tr> <td>[16]</td> <td class="space">Désidéri, J.-A.; Glowinski, R.; Périaux, J., Hypersonic Flows for Reentry Problems (1990)</td> </tr><tr> <td>[17]</td> <td class="space">Edney, B., Anomalous Heat Transfer and Pressure Distributions on Blunt Bodies at Hypersonic Speeds in the Presence of an Impinging Shock (1968)</td> </tr><tr> <td>[18]</td> <td class="space">Edwards, W. S.; Tuckerman, L. S.; Friesner, R. A.; Sorensen, D. C., Krylov methods for the incompressible Navier-Stokes equations, J. Comput. Phys., 110, 82 (1994) · <a href="/0792.76062" class="nowrap">Zbl 0792.76062</a></td> </tr><tr> <td>[20]</td> <td class="space">Fezoui, L.; Lanteri, S.; Larrouturou, B.; Olivier, C., Resolution Numerique des Equations de Navier-Stokes pour un Fluide Compressible en Maillage Triangulaire (1989)</td> </tr><tr> <td>[22]</td> <td class="space">Freund, R. W., Conjugate gradient-type methods for linear systems with complex symmetric coefficient matrices, SIAM J. Sci. Stat. Comp., 13, 425 (1992) · <a href="/0761.65018" class="nowrap">Zbl 0761.65018</a></td> </tr><tr> <td>[23]</td> <td class="space">Freund, R. W., A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems, SIAM J. Sci. Comp., 14, 470 (1993) · <a href="/0781.65022" class="nowrap">Zbl 0781.65022</a></td> </tr><tr> <td>[24]</td> <td class="space">Freund, R. W.; Nachtigal, N. M., QMR: A quasi-minimal residual method for non-Hermitian linear systems, Numer. Math., 60, 315 (1991) · <a href="/0754.65034" class="nowrap">Zbl 0754.65034</a></td> </tr><tr> <td>[25]</td> <td class="space">Friedrich, O., A new method for generating inner points of triangulations in two dimensions, Comp. Meth. Appl. Mech. and Eng., 104, 77 (1993) · <a href="/0771.76056" class="nowrap">Zbl 0771.76056</a></td> </tr><tr> <td>[26]</td> <td class="space">Friedrich, O.; Hempel, D.; Meister, A.; Sonar, Th., Adaptive computation of unsteady flow fields with the DLR-\(T, 77\) th AGARD Fluid Dynamics Panel Meeting and Symposium on Progress and Challenges in CFD Methods and Algorithms (1995)</td> </tr><tr> <td>[27]</td> <td class="space">Gaitonde, A. L., A dual-time method for the solution of the unsteady Euler equations, The Aeronautical Journal of the Royal Aeronautical Society, 98, 283 (1994)</td> </tr><tr> <td>[28]</td> <td class="space">Godunov, S. K., A finite difference method for the numerical computation of discontinuous solutions of the equations of fluid dynamics, Mat. Sb., 47, 357 (1959)</td> </tr><tr> <td>[29]</td> <td class="space">Golub, G.; Greenbaum, A.; Luskin, M., Transpose-Free Quasi-Minimal Residual Methods for Non-Hermitian Linear Systems, 60 (1994) · <a href="/0804.65032" class="nowrap">Zbl 0804.65032</a></td> </tr><tr> <td>[30]</td> <td class="space">Gutknecht, M. H., Variants of BiCGSTAB for matrices with complex spextrum, SIAM J. Sci. Comp., 14, 1020 (1993) · <a href="/0837.65031" class="nowrap">Zbl 0837.65031</a></td> </tr><tr> <td>[31]</td> <td class="space">Hackbusch, W., Multi-Grid Methods and Applications, 4 (1985) · <a href="/0585.65030" class="nowrap">Zbl 0585.65030</a></td> </tr><tr> <td>[32]</td> <td class="space">Hänel, D.; Schwane, R., An implicit flux-vector splitting scheme for the computation of viscous hypersonic flow, AIAA Paper (1989)</td> </tr><tr> <td>[33]</td> <td class="space">Hänel, D.; Schwane, R.; Seider, G., On the accuracy of upwind schemes for the solution of the Navier-Stokes equations, AIAA Paper, 87-1105 (1987)</td> </tr><tr> <td>[34]</td> <td class="space">Hannemann, V., Numerische Simulation von Stoss-Stoss-Wechselwirkungen unter Berücksichtigung von chemischen und thermischen Nichtgleichgewichtseffekten (1996)</td> </tr><tr> <td>[35]</td> <td class="space">Hannemann, V.; Hempel, D.; Sonar, Th., Dynamic adaptivity and residual control in unsteady compressible flow computation, Mathematical and Computer Modelling, 20, 201 (1994) · <a href="/0816.76073" class="nowrap">Zbl 0816.76073</a></td> </tr><tr> <td>[36]</td> <td class="space">Hempel, D., Isotropic refinement and recoarsening in two dimensions, Numerical Algorithms, 13, 33 (1996) · <a href="/0861.65102" class="nowrap">Zbl 0861.65102</a></td> </tr><tr> <td>[37]</td> <td class="space">Hestenes, M. R.; Stiefel, E., Methods of conjugate gradients for solving linear systems, NBS J. Res., 49, 409 (1952) · <a href="/0048.09901" class="nowrap">Zbl 0048.09901</a></td> </tr><tr> <td>[38]</td> <td class="space">Hietel, D.; Meister, A.; Sonar, Th., On the comparison of four different implementations of an third-order ENO scheme of box type for the computation of compressible flow, Numerical Algorithms, 13, 77 (1996) · <a href="/0865.76052" class="nowrap">Zbl 0865.76052</a></td> </tr><tr> <td>[39]</td> <td class="space">Hilgenstock, A., The ViB-Code to Simulate 3-D Stator/Rotor Flow in Axial Turbines (1992)</td> </tr><tr> <td>[40]</td> <td class="space">Hirsch, C., Numerical Computation of Internal and External Flows, 2 (1988) · <a href="/0662.76001" class="nowrap">Zbl 0662.76001</a></td> </tr><tr> <td>[41]</td> <td class="space">Holden, M. S.; Wieting, A. R.; Moselle, J. R.; Glass, C., Studies of aerothermal loads generated in regions of shock/shock interaction in hypersonic flow, AIAA 26th Aerospace Sciences Meeting (January 1988)</td> </tr><tr> <td>[42]</td> <td class="space">Issman, E.; Degrez, G., Implicit iterative methods for a multidimensional upwind Euler/Navier-Stokes solver on unstructured grids, Von Karman Institute for Fluid Dynamics, Lecture Series (March 1995)</td> </tr><tr> <td>[43]</td> <td class="space">Jameson, A., Comm. Pure Appl. Math., 41, 507 (1988) · <a href="/0681.76064" class="nowrap">Zbl 0681.76064</a></td> </tr><tr> <td>[44]</td> <td class="space">Joubert, W., Lanczos methods for the solution of nonsymmetric systems of linear equations, SIAM J. Matrix Anal. Appl., 13, 926 (1992) · <a href="/0758.65026" class="nowrap">Zbl 0758.65026</a></td> </tr><tr> <td>[45]</td> <td class="space">Kasenally, E. M., Gmback: A generalised minimum backward error algorithm for nonsymmetric linear systems, SIAM J. Sci. Comp., 16, 698 (1995) · <a href="/0823.65029" class="nowrap">Zbl 0823.65029</a></td> </tr><tr> <td>[46]</td> <td class="space">LeVeque, R. J., Numerical Methods for Conservation Laws (1990) · <a href="/0682.76053" class="nowrap">Zbl 0682.76053</a></td> </tr><tr> <td>[47]</td> <td class="space">Liou, M.-S.; Steffen, C. J., A New Flux Splitting Scheme (May 1991)</td> </tr><tr> <td>[48]</td> <td class="space">Liou, M.-S.; Steffen, C. J., J. Comput. Phys., 107, 23 (1993) · <a href="/0779.76056" class="nowrap">Zbl 0779.76056</a></td> </tr><tr> <td>[49]</td> <td class="space">Meister, A., Zur Verwendung der Mehrgittermethode bei der zeitgenauen Lösung der instationären Eulergleichungen (1993)</td> </tr><tr> <td>[50]</td> <td class="space">Meister, A., Ein Beitrag zum DLR-\(T (1994)\)</td> </tr><tr> <td>[52]</td> <td class="space">Meister, A., Zur zeitgenauen numerischen Simulation reibungsbehafteter, kompressibler, turbulenter Strömungsfelder mit einer impliziten Finite-Volumen-Methode vom Box-Typ (1996) · <a href="/0863.76053" class="nowrap">Zbl 0863.76053</a></td> </tr><tr> <td>[53]</td> <td class="space">Meister, A.; Oevermann, M., Computation of laminar and turbulent compressible flow fields on unstructured grids with an implicit finite volume scheme, Proceedings of the 2nd Seminar on Euler and Navier-Stokes Equations (1996)</td> </tr><tr> <td>[54]</td> <td class="space">Nachtigal, N. M.; Reddy, S. C.; Trefethen, L. N., How fast are nonsymmetric matrix iterations?, SIAM J. Matrix Anal. Appl., 13, 778 (1992) · <a href="/0754.65036" class="nowrap">Zbl 0754.65036</a></td> </tr><tr> <td>[55]</td> <td class="space">Nagaoka, M.; Horinouchi, N., Implicit compressible flow solvers on unstructured meshes, Comput. Fluid Dynamics J., 2, 169 (1993)</td> </tr><tr> <td>[56]</td> <td class="space">Osher, S.; Solomon, F., Upwind schemes for hyperbolic systems of conservation laws, Math. Comput., 38, 339 (1982) · <a href="/0483.65055" class="nowrap">Zbl 0483.65055</a></td> </tr><tr> <td>[57]</td> <td class="space">Pommerall, C.; Fichtner, W., memory aspects and performance of iterative solvers, SIAM J. Sci. Comput., 15, 460 (1994) · <a href="/0798.65045" class="nowrap">Zbl 0798.65045</a></td> </tr><tr> <td>[59]</td> <td class="space">Radicati, G.; Robert, Y.; Succi, S., Iterative algorithms for the solution of nonsymmetric systems in the modelling of weak plasma turbulence, J. Comput. Phys., 80, 489 (1989) · <a href="/0659.76126" class="nowrap">Zbl 0659.76126</a></td> </tr><tr> <td>[60]</td> <td class="space">Roe, P. L., Approximate riemann solvers, parameter vectors, and difference schemes, J. Comput. Phys., 43, 357 (1981) · <a href="/0474.65066" class="nowrap">Zbl 0474.65066</a></td> </tr><tr> <td>[61]</td> <td class="space">Saad, Y., Preconditioning techniques for nonsymmetric and indefinite linear systems, Journal of Comp. and Appl. Math., 24, 89 (1988) · <a href="/0662.65028" class="nowrap">Zbl 0662.65028</a></td> </tr><tr> <td>[62]</td> <td class="space">Saad, Y., A flexible inner-outer preconditioned GMRES algorithm, SIAM J. Sci. Comp., 14, 461 (1993) · <a href="/0780.65022" class="nowrap">Zbl 0780.65022</a></td> </tr><tr> <td>[63]</td> <td class="space">Saad, Y., Krylov subspace techniques, conjugate gradients, preconditioning and sparse matrix solvers, von Karman Institute of Fluid Dynamics, Lecture series (1994)</td> </tr><tr> <td>[64]</td> <td class="space">Saad, Y., Iterative Methods for Sparse Linear Systems (1996) · <a href="/1002.65042" class="nowrap">Zbl 1002.65042</a></td> </tr><tr> <td>[65]</td> <td class="space">Saad, Y.; Schultz, M. H., Conjugate gradient-like algorithms for solving nonsymmetric linear systems, Math. Comput., 44, 417 (1985) · <a href="/0566.65019" class="nowrap">Zbl 0566.65019</a></td> </tr><tr> <td>[66]</td> <td class="space">Saad, Y.; Schultz, M. H., GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Stat. Comp., 856 (1986) · <a href="/0599.65018" class="nowrap">Zbl 0599.65018</a></td> </tr><tr> <td>[67]</td> <td class="space">Saunders, M. A.; Simon, H. D.; Yip, E. L., Two conjugate-gradient-type methods for unsymmetric linear equations, SIAM J. Numer. Anal., 25, 927 (1988) · <a href="/0652.65022" class="nowrap">Zbl 0652.65022</a></td> </tr><tr> <td>[68]</td> <td class="space">Slack, D. C.; Whitaker, D. L.; Walters, R. W., Time integration algorithms for the two-dimensional Euler equations on unstructured meshes, AIAA J., 32, 1158 (1994) · <a href="/0821.76064" class="nowrap">Zbl 0821.76064</a></td> </tr><tr> <td>[69]</td> <td class="space">Sleijpen, G. L.G.; Fokkema, D. R., Bicgstab \((l\), Electronic Transactions on Numerical Analysis, 1, 11 (1993) · <a href="/0820.65016" class="nowrap">Zbl 0820.65016</a></td> </tr><tr> <td>[70]</td> <td class="space">Sonar, Th., On the design of an upwind scheme for compressible flow on general triangulations, Numerical Algorithms, 4, 135 (1993) · <a href="/0765.76066" class="nowrap">Zbl 0765.76066</a></td> </tr><tr> <td>[71]</td> <td class="space">Sonneveld, P., CGS: A fast Lanczos-type solver for nonsymmetric linear systems, SIAM J. Sci. Stat. Comput., 10, 36 (1989) · <a href="/0666.65029" class="nowrap">Zbl 0666.65029</a></td> </tr><tr> <td>[72]</td> <td class="space">Steger, J. L.; Warming, R. F., Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods, J. Comput. Phys., 40, 263 (1981) · <a href="/0468.76066" class="nowrap">Zbl 0468.76066</a></td> </tr><tr> <td>[73]</td> <td class="space">van der Vorst, H. A., The convergence behaviour of preconditioned CG and CG-S in the presence of rounding errors, Lecture Notes in Mathematics, 1457, 126 (1990) · <a href="/0714.65034" class="nowrap">Zbl 0714.65034</a></td> </tr><tr> <td>[74]</td> <td class="space">van der Vorst, H. A., Bi-cgstab: A fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems, SIAM J. Sci. Stat. Comput., 13, 631 (1992) · <a href="/0761.65023" class="nowrap">Zbl 0761.65023</a></td> </tr><tr> <td>[75]</td> <td class="space">van der Vorst, H. A.; Dekker, K., Conjugate gradient type methods and preconditioning, J. Comp. Appl. Math., 24, 73 (1988) · <a href="/0659.65033" class="nowrap">Zbl 0659.65033</a></td> </tr><tr> <td>[77]</td> <td class="space">Venkatakrishnan, V., Implicit Schemes and Parrallel Computing in Unstructured Grid CFD (1995)</td> </tr><tr> <td>[78]</td> <td class="space">Venkatakrishnan, V.; Mavriplis, D. J., Implicit solver for unstructured meshes, J. Comput. Phys., 105, 83 (1993) · <a href="/0783.76065" class="nowrap">Zbl 0783.76065</a></td> </tr><tr> <td>[79]</td> <td class="space">Wada, Y.; Liou, M.-S., A flux splitting scheme with high-resolution and robustness for discontinuities, AIAA Paper (1994)</td> </tr><tr> <td>[80]</td> <td class="space">Waidmann, W.; Alff, F.; Böhm, M.; Brummund, U.; Clauss, W.; Oschwald, M., Supersonic combustion of hydrogen/air in a SCRAMJET combustion chamber, 45th Conference of the International Astronautical Federation (1994)</td> </tr><tr> <td>[81]</td> <td class="space">Walker, H. F., Implementation of the GMRES method using householder transformations, SIAM J. Sci. Comp., 9, 152 (1988) · <a href="/0698.65021" class="nowrap">Zbl 0698.65021</a></td> </tr><tr> <td>[82]</td> <td class="space">Wieting, A. R.; Holden, M. S., Experimental study of shock wave interference heating on a cylindrical leading edge at mach 6 and 8, AIAA 22nd Thermophysics Conference (June 1987)</td> </tr><tr> <td>[83]</td> <td class="space">Xu, J.; Cai, X., A preconditioned GMRES method for nonsymmetric or indefinite problems, Math. Comp., 59, 311 (1992) · <a href="/0766.65034" class="nowrap">Zbl 0766.65034</a></td> </tr></table> <div class="reference_disclaimer"> 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>