compressible Navier-Stokes flow solver using the Newton-Krylov method on unstructured grids.
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compressible Navier-Stokes flow solver using the Newton-Krylov method on unstructured grids.

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Published .
Written in English


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A Newton-Krylov algorithm is presented for the compressible Navier-Stokes equations on hybrid unstructured grids. The Spalart-Allmaras turbulence model is used for turbulent flows. The spatial discretization is based on a finite-volume matrix dissipation scheme. A preconditioned matrix-free generalized minimal residual method is used to solve the linear system that arises in the Newton iterations. The incomplete lower-upper factorization based on an approximate Jacobian is used as the preconditioner after applying the reverse Cuthill-McKee reordering. Various aspects of the Newton-Krylov algorithm are studied to improve efficiency and reliability. The inexact Newton method is studied to avoid over-solving of the linear system to reduce computational cost. The ILU(1) approach is selected in three dimensions, based on a comparison among various preconditioners. Approximate viscous formulations involving only the nearest neighboring terms are studied to reduce the cost of preconditioning. The resulting preconditioners are found to be effective and provide Newton-type convergence. Scaling of the linear system is studied to improve convergence of the inexact matrix-free approach. Numerical studies are performed for two-dimensional cases as well as flows over the ONERA M6 wing and the DLR-F6 wing-body configuration. A ten-order-of-magnitude residual reduction can be obtained with a computing cost equivalent to 4,000 residual function evaluations for two-dimensional cases, while the same convergence can be obtained in 5,500 and 8,000 function evaluations for the wing and wing-body configuration, respectively, on grids with a half million nodes.

The Physical Object
Pagination134 leaves.
Number of Pages134
ID Numbers
Open LibraryOL21549251M
ISBN 109780494217672

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T. J. Barth, S. W. Linton: An Unstructured Mesh Newton Solver for Compressible Fluid Flow and Its Parallel Implementation, AIAA conference paper , () Google Scholar 4. M. Blanco, D. W. Zingg: A Fast Solver for the Euler Equations on Unstructured Grids Using a Newton-GMRES Method, AIAA conference paper , () Google ScholarAuthor: Amir Nejat, Carl Ollivier-Gooch. A Newton-Krylov flow solver is presented for the Euler equations on unstructured grids. The algorithm uses a preconditioned matrix-free GMRES method to . The finite volume method (FVM) is the most widely used numerical method by computational fluid dynamics (CFD) researchers to solve the compressible Navier-Stokes equations. A successful FVM solver should be accurate, efficient and robust. High-order spatial discretization must be Cited by: 3. () A new numerical method for solution of boiling flow using combination of SIMPLE and Jacobian-free Newton-Krylov algorithms. Progress in Nuclear Ene () On the plastic driving force of grain boundary migration: A fully coupled phase field and crystal plasticity model.

Navier-Stokes right-hand side and of its Jacobian, without inversion of the viscous operator. Time evolution is performed by a nonlinear extension of the method of exponential propagation. Steady states are calculated by inexact Krylov-Newton iteration using ORTHORES and GMRES. Study on Hypersonic Finite-Rate Chemically Reacting Flows Using Upwind Method p. Study of the Erosion of Stably Stratified Medium Heated from Below p. Advances in Euler and Navier-Stokes Methods for Helicopter Applications p. Numerical Simulation of Unsteady Compressible Viscous Flow NACA Airfoil-Vortex Interaction p. Using dual time stepping, the above mentioned multigrid method can be used for unsteady flows. This results in a good method for Euler flows, but for the Navier-Stokes equations, dual time stepping was observed to be very slow for some cases, in particular for turbulent flows on high aspect ratio grids. American Institute of Aeronautics and Astronautics Sunrise Valley Drive, Suite Reston, VA

@article{osti_, title = {Newton-Krylov-Schwarz methods for aerodynamics problems: compressible and incompressible flows on unstructured grids.}, author = {Kaushik, D K and Keyes, D E and Smith, B F}, abstractNote = {We review and extend to the compressible regime an earlier parallelization of an implicit incompressible unstructured Euler code [9], and solve for flow over an . - Fully unstructured grids (triangles, quads, or mixed) - Least-squares gradients (linear or quadratic LSQ) - Diffusion is discretized as a hyperbolic system for accurate gradient prediction - Implicit time-stepping with BDF2 - Jacobian-Free Newton-Krylov with GCR - Defect-correction implicit solver as a variable preconditioner. A three-dimensional Newton-Krylov Navier-Stokes flow solver using a one-equation turbulence model, Master’s thesis, University of Toronto, Toronto, Ontario, Canada, 31 Kim, D. B. and Orkwis, P. D., “Jacobian update strategies for quadratic and near-quadratic convergence of Newton and. () On Newton–Krylov Multigrid Methods for the Incompressible Navier–Stokes Equations. Journal of Computational Physics , () A reduced degree of freedom method for simulating non-isothermal multi-phase flow in a porous medium.