A High-Order Parallel Newton-Krylov Flow Solver for the Euler Equations

Abstract

This work presents a parallel Newton-Krylov flow solver employing third and fourthorder spatial discretizations to solve the three-dimensional Euler equations on structured multi-block meshes. The fluxes are discretized using summation-by-parts operators; boundary and interface conditions are implemented using simultaneous approximation terms. Functionals, drag and lift, are calculated using Simpson's rule. The solver is verified using the method of manufactured solutions and Ringleb flow and validated using the ONERA M6 wing. The results demonstrate that the combination of high-order finite-difference operators with a parallel Newton-Krylov solution technique is an excellent option for efficient computation of aerodynamic flows.

A parallel Newton-Krylov-Schur flow solver for the Reynolds-Averaged Navier-Stokes equations

“…A few examples of popular RANS solvers are OVERFLOW, 1 FUN3D, 2 Flo3xx, 3 and NSU3D. 4 This paper presents an efficient parallel three-dimensional multi-block structured solver for turbulent flows over aerodynamic geometries, extending previous work 5,6,7 on an efficient parallel Newton-Krylov flow solver for the Euler equations and the Navier-Stokes equations in the laminar flow regime.…”

“…However, SATs have received limited use in computational aerodynamics applications, and there are only a few demonstrations of their use for practical aerodynamic problems. 5,6,7,15 They present a difficulty in that they can necessitate the use of small time steps with explicit solvers. 16 Hence, the combination of SATs with a parallel Newton-Krylov solver has the potential to be an efficient approach.…”

Weak and strong wall boundary procedures and convergence to steady-state of the Navier–Stokes equations

“…The main reason to use weak boundary procedures stems from the fact that together with summation-by-parts operators they lead to provable stable schemes. For application of this technique to finite difference methods, node-centered finite volume methods, spectral domain methods and various hybrid methods see [25,42,4,30,31,36,44,48,20,39,6,22,13,24], [32,47,45,46,14,41], [18,16,19,7] and [33,34,15,37,5] respectively. In this paper we will consider a new effect of using weak boundary procedures, namely that it in many cases (all that we tried) speeds up the convergence to steady-state.…”

Advances in Homotopy Continuation Methods in Computational Fluid Dynamics

“…22,40 Our own analysis of these parameters on mesh 1a also indicates that the solver is fast and robust under the following parameters: a = 0.01, b = 1.5, ILU(0) for globalization phase updated ever 3 iterations, ILU(1) in the inexact Newton phase (INP) updated every iteration, linear solver relative tolerance of 0.05, µ rel = 1/15. Furthermore, the solution update at each nonlinear iteration of the globalization phase is relaxed by a factor of 0.6 for additional stability.…”