An adaptive multiscale finite volume solver for unsteady and steady state flow computations

Bramkamp, F.; Lamby, Ph.; Müller, Siegfried

doi:10.1016/j.jcp.2003.12.005

Cited by 106 publications

(105 citation statements)

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“…For the numerical simulation of the compressible Euler equations we use the software package QUADFLOW, which is currently under development at Aachen University, cf. [5,9,10,11,39]. We briefly describe a few main features of this solver.…”

Section: Discrete Euler Equationsmentioning

confidence: 99%

“…Details are given in [11]. Note that in general a smaller timestep will improve the condition number of the approximate Jacobian in (3).…”

Section: Discrete Euler Equationsmentioning

confidence: 99%

“…The maximum CFL-number was set to γ max = 1000. Computations are done as in [11]: We allow 8 maximum levels of refinement. In the cases A and C 10 cycles of adaptations are performed, 13 levels are used in case B.…”

Section: Test Problem 1: Stationary Flow Around Naca0012 Airfoilmentioning

confidence: 99%

“…A method of this class has been implemented in the QUADFLOW package, which is an adaptive multiscale finite volume solver for stationary and instationary compressible flow computations. Descriptions of this solver are given in [5,9,10,11,39]. For the linearization we use a standard (approximate) Newton method.…”

Section: Introductionmentioning

confidence: 99%

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Numbering techniques for preconditioners in iterative solvers for compressible flows

Pollul

Reusken

2007

Numerical Methods in Fluids

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We consider Newton-Krylov methods for solving discretized compressible Euler equations. A good preconditioner in the Krylov subspace method is crucial for the efficiency of the solver. In this paper we consider a point-block Gauss-Seidel method as preconditioner. We describe and compare renumbering strategies that aim at improving the quality of this preconditioner. A variant of reordering methods known from multigrid for convection-dominated elliptic problems is introduced. This reordering algorithm is essentially black-box and significantly improves the robustness and efficiency of the point-block Gauss-Seidel preconditioner. Results of numerical experiments using the QUADFLOW solver and the PETSc library are given.

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Section: Discrete Euler Equationsmentioning

confidence: 99%

“…Details are given in [11]. Note that in general a smaller timestep will improve the condition number of the approximate Jacobian in (3).…”

Section: Discrete Euler Equationsmentioning

confidence: 99%

Section: Test Problem 1: Stationary Flow Around Naca0012 Airfoilmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Numbering techniques for preconditioners in iterative solvers for compressible flows

Pollul

Reusken

2007

Numerical Methods in Fluids

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“…Applications that use multiscale analysis [2] like Quadflow [3] or adaptive mesh refinement (AMR) [4] often exhibit evolving behavior typically due to unexpected increases in computations or having reached hardware limits (e.g., memory) on a node. Finally, the fourth class of jobs is called the malleable job.…”

Section: Introductionmentioning

confidence: 99%

A Batch System with Efficient Adaptive Scheduling for Malleable and Evolving Applications

Prabhakaran

Neumann

Rinke

et al. 2015

2015 IEEE International Parallel and Distributed Processing Symposium

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Abstract-The throughput of supercomputers depends not only on efficient job scheduling but also on the type of jobs that form the workload. Malleable jobs are most favorable for a cluster as they can dynamically adapt to a changing allocation of resources. The batch system can expand or shrink a running malleable job to improve system utilization, throughput, and response times. In the past, however, the rigid nature of commonly used programming models like MPI made writing malleable applications a daunting task, which is why it remained largely unrealized. This is now changing. To improve fault tolerance, load imbalance, and energy efficiency in emerging exascale systems, more adaptive programming paradigms such as Charm++ enter the scene. Although they offer better support for malleability, current batch systems still lack management facilities for malleable jobs and are therefore incapable of leveraging their potential. In this paper, we present an extension of the Torque/Maui batch system for malleability. We propose a novel malleable job scheduling strategy and show the first batch system capable of efficiently managing rigid, malleable, and evolving jobs together. We demonstrate that our strategy achieves consistently superior performance in comparison to every other state-of-the-art malleable job scheduling strategy under varying dynamics of the workload.

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On adaptive timestepping for weakly instationary solutions of hyperbolic conservation laws via adjoint error control

Steiner

Noelle

2008

Numer Methods Biomed Eng

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Abstract. We study a recent timestep adaptation technique for hyperbolic conservation laws. The key tool is a space-time splitting of adjoint error representations for target functionals due to Süli[19] and Hartmann [13]. It provides an efficient choice of timesteps for implicit computations of weakly instationary flows. The timestep will be very large in regions of stationary flow, and become small when a perturbation enters the flow field. Besides using adjoint techniques which are already well-established, we also add a new ingredient which simplifies the computation of the dual problem. Due to Galerkin orthogonality, the dual solution ϕ does not enter the error representation as such. Instead, the relevant term is the difference of the dual solution and its projection to the finite element space, ϕ − ϕ h . We can show that it is therefore sufficient to compute the spatial gradient of the dual solution, w = ∇ϕ. This gradient satisfies a conservation law instead of a transport equation, and it can therefore be computed with the same algorithm as the forward problem, and in the same finite element space. We demonstrate the capabilities of the approach for a weakly instationary test problem for scalar conservation laws.

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An adaptive multiscale finite volume solver for unsteady and steady state flow computations

Cited by 106 publications

References 50 publications

Numbering techniques for preconditioners in iterative solvers for compressible flows

Numbering techniques for preconditioners in iterative solvers for compressible flows

A Batch System with Efficient Adaptive Scheduling for Malleable and Evolving Applications

On adaptive timestepping for weakly instationary solutions of hyperbolic conservation laws via adjoint error control

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