Fast unsteady flow computations with a Jacobian-free Newton–Krylov algorithm

Lucas, Peter; Zuijlen, A.H. van; Bijl, H.

doi:10.1016/j.jcp.2010.08.033

Cited by 19 publications

(8 citation statements)

References 25 publications

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“…Blocking the flow variables in this way, also referred to as "field interlacing" in the literature, is acknowledged [7][8][9] to result in better performances than grouping variables per aerodynamic quantity.…”

Section: Space Discretisationmentioning

confidence: 99%

Multilevel Variable-Block Schur-Complement-Based Preconditioning for the Implicit Solution of the Reynolds- Averaged Navier-Stokes Equations Using Unstructured Grids

Carpentieri¹,

Bonfiglioli²

2018

Computational Fluid Dynamics - Basic Instruments and Applications in Science

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Implicit methods based on the Newton's rootfinding algorithm are receiving an increasing attention for the solution of complex Computational Fluid Dynamics (CFD) applications due to their potential to converge in a very small number of iterations. This approach requires fast convergence acceleration techniques in order to compete with other conventional solvers, such as those based on artificial dissipation or upwind schemes, in terms of CPU time. In this chapter, we describe a multilevel variable-block Schur-complement-based preconditioning for the implicit solution of the Reynoldsaveraged Navier-Stokes equations using unstructured grids on distributed-memory parallel computers. The proposed solver detects automatically exact or approximate dense structures in the linear system arising from the discretization, and exploits this information to enhance the robustness and improve the scalability of the block factorization. A complete study of the numerical and parallel performance of the solver is presented for the analysis of turbulent Navier-Stokes equations on a suite of threedimensional test cases.

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Section: Space Discretisationmentioning

confidence: 99%

Multilevel Variable-Block Schur-Complement-Based Preconditioning for the Implicit Solution of the Reynolds- Averaged Navier-Stokes Equations Using Unstructured Grids

Carpentieri¹,

Bonfiglioli²

2018

Computational Fluid Dynamics - Basic Instruments and Applications in Science

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“…Таким об-разом, элементы матрицыÃ col зависят от параметров ξ и h. Для того, чтобы полу-чить матрицуÃ col , состоящую только из числовых элементов, задавались числовые значения полушага сетки h по формуле h = 0. (18), (11), (12). Тогда можно представить всю матрицу A в виде…”

Section: предобуславливатели для метода кннunclassified

On Combining Different Acceleration Techniques at the Iterative Solution of PDEs by the Method of Collocations and Least Residuals

Shapeev¹,

Vorozhtsov²

2017

Model. anal. inf. sist.

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“…It is based on a Jacobian-free NewtonKrylov (JFNK) approach (e.g., see Ref. [17] for a review). Typically, JFNK methods employ a preconditioner, and efficiency of such methods strongly depends on the choice of the preconditioner.…”

Section: Multigrid Techniquesmentioning

confidence: 99%

“…For the inviscid terms in the Jacobian operator, central differences with scaled second-difference artificial dissipation are used. Lucas et al 17 use divided-difference Jacobians and apply some techniques to reduce bandwidth, including lumping and approximations to the viscous terms. We use a preconditioner based on a defect-correction Jacobian approximation 19,20 with an adaptive time step control.…”

Section: Multigrid Techniquesmentioning

confidence: 99%

“…The GCR minimization is over all residuals and because the turbulence residuals are several orders of magnitude higher than the mean-flow residuals, the minimization focuses on the turbulence residuals. A scaling factor for the turbulence residuals within the GCR approach similar to that used by Lucas et al 17 was introduced but generally had little influence on the results. The effect of scaling within the GCR when using tightly-coupled relaxation is shown in table A.2 and indicates no positive benefit.…”

Section: Appendix A: Effect Of Increasing Maximum Cfl With Stmg Solvermentioning

confidence: 99%

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Recent Advances in Agglomerated Multigrid

Nishikawa

Diskin

Thomas

et al. 2013

51st AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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We report recent advancements of the agglomerated multigrid methodology for complex flow simulations on fully unstructured grids. An agglomerated multigrid solver is applied to a wide range of test problems from simple two-dimensional geometries to realistic threedimensional configurations. The solver is evaluated against a single-grid solver and, in some cases, against a structured-grid multigrid solver. Grid and solver issues are identified and overcome, leading to significant improvements over single-grid solvers. I. Nomenclature R Global residual vector II. Introduction Multigrid techniques1, 2 are used to accelerate convergence of current Reynolds-Averaged Navier-Stokes (RANS) solvers for both steady and unsteady flow solutions, particularly for structured-grid applications. Lallemand et al. 3 and Smith 4 introduced Agglomerated Multigrid (AgMG) methods for unstructured-grid applications, and Mavriplis et al. [5][6][7][8] developed AgMG methods for large-scale unstructured-grid applications. The AgMG methods have been implemented in several practical unstructured grid codes and applied to configurations used for the Drag and High Lift Prediction Workshops.9, 10 The AgMG methods accelerated convergence in many instances but problems were encountered, such as grid-dependent convergence to smaller residual levels, discrepancies between single-grid and multigrid solutions, and convergence problems for cases at the edges of the flight envelope. In fact, analysis and systematic computations with these techniques showed convergence degradation on highly-refined grids even for simple model problems. To overcome the difficulty, we critically studied AgMG techniques 11, 12 for isotropic and highly-stretched grids, and developed quantitative analysis methods and computational techniques to achieve fast grid-independent convergence for a model equation representing laminar diffusion in the incompressible limit. It was found that consistent coarse-grid discretizations are essential for * Senior Research Scientist (hiro@nianet.org), National Institute of Aerospace, 100 Exploration Way, Hampton grid-independent multigrid convergence on isotropic grids, 11 and that prismatic cells, line-agglomeration, and line-implicit subiterations are essential for grid-independent multigrid convergence on highly-stretched grids. 12Building upon these fundamental studies, we extended and demonstrated these techniques for inviscid, viscous, and turbulent flow equations over complex geometries using a serial code 13 and a parallel code. 14The developed AgMG method has been shown to provide a significant speedup over a state-of-the-art singlegrid (SG) solver for the complex flows considered in the previous papers. However, several difficulties were encountered when the AgMG method was applied to some other problems. For example, multigrid convergence degraded in the presence of nearly-degenerate stencils on surface grids, grids with a polar singularity, disjoint grids in grid partitioning, etc. In this paper, we probe these and other issue...

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Fast unsteady flow computations with a Jacobian-free Newton–Krylov algorithm

Cited by 19 publications

References 25 publications

Multilevel Variable-Block Schur-Complement-Based Preconditioning for the Implicit Solution of the Reynolds- Averaged Navier-Stokes Equations Using Unstructured Grids

Multilevel Variable-Block Schur-Complement-Based Preconditioning for the Implicit Solution of the Reynolds- Averaged Navier-Stokes Equations Using Unstructured Grids

On Combining Different Acceleration Techniques at the Iterative Solution of PDEs by the Method of Collocations and Least Residuals

Recent Advances in Agglomerated Multigrid

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