Efficient Newton-Krylov Solver for Aerodynamic Computations

Pueyo, Alberto; Zingg, David W.

doi:10.2514/2.326

Cited by 55 publications

(5 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…n mbn=mc, and T n is a diagonal matrix containing the (inverse) local time steps appropriate to each equation. Finally, we emphasize that the update equation (16) is not solved exactly, but rather inexactly, to a relative tolerance of 0.5 using a Krylov iterative solver; the solution of the linear system is discussed further in Sec. III.B.…”

Section: Approximate-newton Phasementioning

confidence: 99%

“…Preconditioners are the most critical component of an efficient parallel linear solver. Although excellent serial preconditioners exist for Newton-Krylov flow solvers [5,16,17], these preconditioners cannot be implemented efficiently in parallel; for example, although using ILUp on the global system matrix A has proven to work well in serial, a parallel version results in substantial idle time and communication. The essence of the challenge is that a good parallel preconditioner must balance the competing objectives of scalability and serial performance.…”

Section: B Solving the Distributed Linear Systemmentioning

confidence: 99%

“…This suggests that a Newton-Krylov solution strategy may be well suited to SAT discretizations. For serial computations, Newton-Krylov solution strategies have proven to be efficient, both in flow simulation [5,[13][14][15][16][17][18] and optimization [4,19]. There are also many examples demonstrating that the excellent serial performance of Newton-Krylov algorithms can be extended to parallel algorithms [20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Parallel Newton-Krylov Solver for the Euler equations Discretized Using Simultaneous Approximation Terms

2008

Self Cite

View full text Add to dashboard Cite

We present a parallel Newton-Krylov algorithm for solving the three-dimensional Euler equations on multiblock structured meshes. The Euler equations are discretized on each block independently using second-order-accurate summation-by-parts operators and scalar numerical dissipation. Boundary conditions are imposed and block interfaces are coupled using simultaneous-approximation terms. The summation-by-parts with simultaneousapproximation-terms approach is time-stable, requires only C 0 mesh continuity at block interfaces, accommodates arbitrary block topologies, and has low interblock-communication overhead. The resulting discrete equations are solved iteratively using an inexact-Newton method. At each Newton iteration, the linear system is solved inexactly using a Krylov-subspace iterative method, and both additive Schwarz and approximate Schur preconditioners are investigated. The algorithm is tested on the ONERA M6 wing geometry. We conclude that the approximate Schur preconditioner is an efficient alternative to the Schwarz preconditioner. Overall, the results demonstrate that the Newton-Krylov algorithm is very efficient: using 24 processors, a transonic flow on a 96-block, 1-million-node mesh requires 12 minutes for a 10-order reduction of the residual norm.

show abstract

Section: Approximate-newton Phasementioning

confidence: 99%

Section: B Solving the Distributed Linear Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Parallel Newton-Krylov Solver for the Euler equations Discretized Using Simultaneous Approximation Terms

2008

Self Cite

View full text Add to dashboard Cite

show abstract

“…The ordering of the unknowns can significantly affect the performance of ILU preconditioning, as was discussed thoroughly in [52] and further elaborated in [52]. It was suggested that reverse Cuthill-McKee (RCM) ordering [53] to be the most effective for the multi-block structured solvers considered in their work.…”

Section: Theory and Mathematical Formulationmentioning

confidence: 99%

A Review of Solution Stabilization Techniques for RANS CFD Solvers

Zhao

et al. 2023

Aerospace

View full text Add to dashboard Cite

Nonlinear, time-linearized and adjoint Reynolds-averaged Navier-Stokes (RANS) computational fluid dynamics (CFD) solvers are widely used to assess and improve the aerodynamic and aeroelastic performance of aircrafts and turbomachines. While RANS CFD solver technologies are relatively mature for applications at design conditions where the flow is benign, their use in off-design conditions, featuring flow instabilities, such as separations and shock wave/boundary layer interactions, still faces many challenges, with tight residual convergence being a major difficulty. To cope with this, several solver stabilization techniques have been proposed. However, a systematic and comparative study of these techniques has not been reported, to some extent hindering the wide deployment of these methods for industrial applications. In this paper, we critically review the existing methods for solver convergence stabilization, with the main purpose of explaining the rationale behind the algorithms and providing a systematic view of the seemingly different methods. Specifically, mathematical formulations and implementation details of these methods, example applications, and the pros and cons of the methods are discussed in detail, along with suggestions for further improvements. This review is expected to give CFD method developers an overview of the various solution stabilization methods and application engineers an idea how to choose a suitable method for their respective applications.

show abstract

“…Both preconditioners require an ILU factorization of the nearest-neighbor approximate Jacobian. This matrix approximates the Jacobian, because it lumps the fourth-difference dissipation into the second-difference dissipation [66]. ILUp [53] with a fill level of 1 is applied locally to each processor's block of the approximate Jacobian to obtain the incomplete factorizations (i.e., the factorization involves no communication).…”

Section: B Newton-krylov Solution Algorithmmentioning

confidence: 99%

Aerodynamic Optimization Algorithm with Integrated Geometry Parameterization and Mesh Movement

2010

Self Cite

View full text Add to dashboard Cite

An efficient gradient-based algorithm for aerodynamic shape optimization is presented. The algorithm consists of several components, including a novel integrated geometry parameterization and mesh movement, a parallel Newton-Krylov flow solver, and an adjoint-based gradient evaluation. To integrate geometry parameterization and mesh movement, generalized B-spline volumes are used to parameterize both the surface and volume mesh. The volume mesh of B-spline control points mimics a coarse mesh; a linear elasticity mesh-movement algorithm is applied directly to this coarse mesh and the fine mesh is regenerated algebraically. Using this approach, mesh-movement time is reduced by two to three orders of magnitude relative to a node-based movement. The mesh-adjoint system also becomes smaller and is thus amenable to complex-step derivative approximations. When solving the flow-adjoint equations using restarted Krylov-subspace methods, a nested-subspace strategy is shown to be more robust than truncating the entire subspace. Optimization is accomplished using a sequential-quadratic-programming algorithm. The effectiveness of the complete algorithm is demonstrated using a lift-constrained induced-drag minimization that involves large changes in geometry.

show abstract

Efficient Newton-Krylov Solver for Aerodynamic Computations

Cited by 55 publications

References 16 publications

Parallel Newton-Krylov Solver for the Euler equations Discretized Using Simultaneous Approximation Terms

Parallel Newton-Krylov Solver for the Euler equations Discretized Using Simultaneous Approximation Terms

A Review of Solution Stabilization Techniques for RANS CFD Solvers

Aerodynamic Optimization Algorithm with Integrated Geometry Parameterization and Mesh Movement

Contact Info

Product

Resources

About