Choice of Variables and Preconditioning for Time Dependent Problems

Turkel, Eli; Vatsa, Veer N.

doi:10.2514/6.2003-3692

Cited by 11 publications

(7 citation statements)

References 15 publications

(14 reference statements)

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“…Detailed historical accounts of the subject can be found in [34], along with a broad number of references for further reading. In connection to the stability analysis performed below, let us point out that the research of numerical algorithms valid for all flow speeds is a very active field [15,24,35,42].…”

mentioning

confidence: 99%

Low Mach Number Limit of the Full Navier-Stokes Equations

Alazard

2005

Arch. Rational Mech. Anal.

242

228

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Abstract. The low Mach number limit for classical solutions to the full Navier Stokes equations is here studied. The combined effects of large temperature variations and thermal conduction are accounted. In particular we consider general initial data. The equations lead to a singular problem, depending on a small scaling parameter, whose linearized is not uniformly well-posed. Yet, it is proved that the solutions exist and are uniformly bounded for a time interval which is independent of the Mach number Ma ∈ (0, 1] , the Reynolds number Re ∈ [1, +∞] and the Péclet number Pe ∈ [1, +∞] . Based on uniform estimates in Sobolev spaces, and using a Theorem of G. Métivier and S. Schochet [31], we next prove that the penalized terms converge strongly to zero. It allows us to rigorously justify, at least in the whole space case, the well-known computations given in the introduction of the P.-L. Lions' book [26].

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confidence: 99%

Low Mach Number Limit of the Full Navier-Stokes Equations

Alazard

2005

Arch. Rational Mech. Anal.

242

228

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“…For steady RANS, the implicit integration method by Weiss et al [24] iterates the numerical solution to a converged steady state. For time-dependent RANS, the implicit time-marching method by Pandya et al [25] and Turkel and Vatsa [26] is used. One blade pitch rotation is produced by integrating over 20 time steps.…”

Section: Methodsmentioning

confidence: 99%

Numerical Optimization of a Stall Margin Enhancing Recirculation Channel for an Axial Compressor

Kawase

Rona

2019

Fluids

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A proof of concept is provided by computational fluid dynamic simulations of a new recirculating type casing treatment. This treatment aims at extending the stable operating range of highly loaded axial compressors, so to improve the safety of sorties of high-speed, high-performance aircraft powered by high specific thrust engines. This casing treatment, featuring an axisymmetric recirculation channel, is evaluated on the NASA rotor 37 test case by steady and unsteady Reynolds Averaged Navier Stokes (RANS) simulations, using the realizable k-ε model. Flow blockage at the recirculation channel outlet was mitigated by chamfering the exit of the recirculation channel inner wall. The channel axial location from the rotor blade tip leading edge was optimized parametrically over the range −4.6% to 47.6% of the rotor tip axial chord c z . Locating the channel at 18.2% c z provided the best stall margin gain of approximately 5.5% compared to the untreated rotor. No rotor adiabatic efficiency was lost by the application of this casing treatment. The investigation into the flow structure with the recirculating channel gave a good insight into how the new casing treatment generates this benefit. The combination of stall margin gain at no rotor adiabatic efficiency loss makes this design attractive for applications to high-speed gas turbine engines.

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“…The second solution strategy is low-Mach preconditioning in which the governing equations are modified to specifically tackle the aforementioned deficiencies. The system preconditioning techniques [38] decrease the acoustic wave speed close to the advection speed by altering the characteristics of the system. This procedure allows a much larger explicit time-step to be taken, but the temporal accuracy is lost unless the approach is combined with the dual time stepping technique [39,38].…”

Section: Incompressible Flowsmentioning

confidence: 99%

“…The system preconditioning techniques [38] decrease the acoustic wave speed close to the advection speed by altering the characteristics of the system. This procedure allows a much larger explicit time-step to be taken, but the temporal accuracy is lost unless the approach is combined with the dual time stepping technique [39,38]. In addition to preconditioning the system, numerical flux preconditioners i.e.…”

Section: Incompressible Flowsmentioning

confidence: 99%

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High-Order Incompressible Computational Fluid Dynamics on Modern Hardware Architectures

Loppi¹

2021

Preprint

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Modern GPU architectures are characterised by an abundance of compute capability relative to memory bandwidth. This makes them very well-suited to solving temporally explicit and spatially compact discretisations of hyperbolic conservation laws. However, classical pressure-projection-based incompressible Navier–Stokes formulations do not fall into this category. One attractive formulation for solving incompressible problems on modern hardware is the method of artificial compressibility. When combined with explicit dual time stepping and a high-order Flux Reconstruction discretisation, the majority of operations can be cast as arithmetically intensive matrix–matrix multiplications that are well-suited for GPUs. In this seminar, I will present the high-order cross-platform incompressible Navier–Stokes solver in PyFR, together with three explicit convergence acceleration techniques: a polynomial multigrid, a novel locally adaptive pseudo-time stepping approach and novel stability-optimised Runge-Kutta schemes. The solver and the convergence acceleration techniques are validated for a range of turbulent test cases, including a simulation of the DARPA SUBOFF submarine model using hundreds of NVIDIA GPUs.

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Choice of Variables and Preconditioning for Time Dependent Problems

Cited by 11 publications

References 15 publications

Low Mach Number Limit of the Full Navier-Stokes Equations

Low Mach Number Limit of the Full Navier-Stokes Equations

Numerical Optimization of a Stall Margin Enhancing Recirculation Channel for an Axial Compressor

High-Order Incompressible Computational Fluid Dynamics on Modern Hardware Architectures

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