Written in English
A three-dimensional multi-block Newton-Krylov flow solver for the Euler equations has been developed for steady aerodynamic flows. The solution is computed through a Jacobian-free inexact-Newton method with an approximate-Newton method for startup. The linear system at each outer iteration is solved using a Generalized Minimal Residual (GMRES) Krylov subspace algorithm. An incomplete lower/upper (ILU) factored preconditioner with reverse Cuthill-Mckee reordering is utilized to increase the efficiency of GMRES.The parameters in the solver are optimized to provide a balance between speed and robustness. Tests are performed using a variety of flow conditions and grid sizes. Results are compared to experimental values and other established numerical solvers. The solver demonstrates fast convergence and accurate solutions on grids up to one million nodes.
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Abstrad A Newton-Krylov Solver for the Euler Equations on Unstructureci Grids Edward Wehner braster of AppM Science Graduate Department of Aerospace Science and Engineering University of Toronto A Newton-Krylov solver for the Euler equations that govern the flow of a compressible invis- cid flow, with application to Bows over aerodynamic conûgwations, is Author: Edward Wehner. A parallel Newton-Krylov ﬂow solver for the Euler equations on multi-block grids Jason E. Hicken∗ and David W. Zingg † Institute for Aerospace Studies, University of Toronto, Toronto, Ontario, M3H 5T6, Canada We present a parallel Newton-Krylov algorithm for solving the three-dimensional Euler equations on multi-block structured meshes. Parallel Newton-Krylov Solver for the Euler equations Discretized Using Simultaneous Approximation Terms. A Three-Dimensional Multi-Block Newton-Krylov Flow Solver for the Euler Equations. A Newton-Krylov Algorithm for the Euler Equations Cited by: A Newton-Krylov flow solver is presented for the Euler equations on unstructured grids. The algorithm uses a preconditioned matrix-free GMRES method to .
Application of Newton-Krylov methodology to a three-dimensional unstructured Euler code. Parallel Newton-Krylov Solver for the Euler equations Discretized Using Simultaneous Approximation Terms. A Three-Dimensional Multi-Block Newton-Krylov Flow Solver for the Euler Equations. vestigated in the context of a parallel Newton-Krylov ﬂow solver for the Euler equations [ 7]. More recently, a comparison has shown that the approximate-Schur preconditioner outperforms the additive-Schwarz pre-conditioner when a large number of processors (>) is used to solve both inviscid and laminar ﬂows [ 4]. This paper presents a three-dimensional Newton-Krylov flow solver for the Navier-Stokes equations which uses summation-by-parts (SBP) operators on . Newton-Krylov ﬂow solver can readily serve as the core of an aerodynamic optimization algorithm, as was demonstrated by Nemec and Zingg for two-dimensional turbulent ﬂow and by Hicken and Zingg for three-dimensional inviscid .
“ A Three-Dimensional Multi-Block Newton–Krylov Flow Solver for the Euler Equations,” 17th AIAA Computational Fluid Dynamics Conference, AIAA Paper , June Link Google Scholar  Blanco M. and Zingg D. W., “ Fast Newton–Krylov Method for Unstructured Grids,” AIAA Journal, Vol. 36, No. 4, , pp. – Cited by: Abstract We present a parallel Newton-Krylov algorithm for solving the three-dimensional Euler equations on multi-block structured meshes. The Euler equations are discretized on each block. A fully implicit Newton–Krylov scheme is used to compute steady state solutions of the Euler equations through their unsteady form. The additional pseudo-time derivative is discretized by a backward Euler step and only one Newton iteration is performed at each pseudo-time step: (1) ℱ u j l + 1 = u j l + 1 − u j l Δ t l + ℛ j l + 1 = 0 Author: I. Lepot, F. Meers, J.-A. Essers. This work presents a parallel Newton-Krylov flow solver employing third and fourth-order spatial discretizations to solve the three-dimensional Euler equations on structured multi-block meshes. The.