Status of multidimensional upwind residual distribution schemes and applications in aeronautics

In this paper we consider the solution of hyperbolic conservation laws on moving meshes by means of an Arbitrary Lagrangian Eulerian (ALE) formulation of the Runge-Kutta Residual Distribution (RD) schemes of Ricchiuto and Abgrall (J Comput Phys 229(16):5653-5691, 2010). Up to the authors knowledge, the problem of recasting RD schemes into ALE framework has been solved with first order explicit schemes and with second order implicit schemes. Our resulting scheme is explicit and second order accurate when computing discontinuous solutions.

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“…Here, we have tested the heuristic definition proposed by Deconinck and co-workers (see e.g. in [29] and references therein)…”

Section: Nonlinear Schemesmentioning

confidence: 99%

An ALE Formulation for Explicit Runge-Kutta Residual Distribution

Abgrall

Arpaia

Ricchiuto

2014

Springer Proceedings in Mathematics &Amp; Statistics

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“…In the present paper adaptation is applied to stationary, advection dominated problems discretized with a node centred residual distribution scheme [54][55][56][57][58]. In all cases unstructured simplex meshes are used.…”

Section: The Flow Solvermentioning

confidence: 99%

“…The solutions on a sequence of uniformly and adaptively refined meshes, have been computed using the Residual Distribution method PSI scheme [54,55,57]. Each simulation was performed using four concurrent computational processes.…”

Section: Burgers Equationmentioning

confidence: 99%

Parallel anisotropic mesh refinement with dynamic load balancing for transonic flow simulations

Gepner

Majewski

Rokicki

2017

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract. The present paper discusses an effective adaptive methods suited for use in parallel environment. An in-house, parallel flow solver based on the residual distribution method is used for the solution of flow problems. Simulation is parallelized based on the domain decomposition approach. Adaptive changes to the mesh are achieved by two distinctive techniques. Mesh refinement is performed by dividing element edges and a subsequent application of pre defined splitting templates. Mesh regularization and derefinement is achieved through topology conserving node movement (r-adaptivity). Parallel implementations of an adaptive use the dynamic load balancing technique.Key words: parallel CFD, adaptation, dynamic load balancing, mesh refinement, parallel efficiency.Parallel anisotropic mesh refinement with dynamic load balancing for transonic flow simulations [28][29][30][31][32]. In general, this approach yields high quality meshes for arbitrarily complex geometries [4,[33][34][35][36]. Nevertheless this approach is difficult to implement in parallel simulations because of the global nature of the remeshing operation.An alternative approach is to apply modifications to the computational mesh only in the regions of interest. Either by local mesh modification operators (edge splits, edge collapses and edge swaps) [37][38][39][40] or element bisection (e.g., based on template refinement) [10,[41][42][43][44][45][46][47]. Locality of these methods makes them especially attractive for application in parallel computing, as the necessary communication volume and frequency become limited, boosting parallel performance.Another possibility is brought by the r-adaptive methods, in which grid nodes are allowed to move without changing the topology of the mesh. This technique is used either to augment local refinement methods [48,49], or as an adaptive tool in itself [50][51][52]. Application of r-adaptive algorithms might be beneficial in parallel computations, as neither the grid topology nor the load balance become affected.Although adaptive methods are well recognised in the academic community, the broader application of adaptation for industrial problems has been limited. This paper presents an approach towards fully parallel and automatic mesh adaptation method that can be used for 3D industrial cases. The h-r adaptive method is developed, suitable for parallel simulation of transonic flows. Adaptivity is accomplished by anisotropic template-based element bisection method. The coarsening step is carried out via an elastic analogy node movement. Anisotropic mesh modifications are driven by a Hessian based approach.

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“…In this work, θ = |φ j,n |/ i∈Cj |(φ j,n i ) N | is chosen [8]. Remark: In order to satisfy the "past-shield" condition, the time-step must be chosen so that k i ≤ 0, which ensures that the distribution is always upwind in time.…”

Section: Space-time Fluctuation Distributionmentioning

confidence: 99%

“…The original formulation, which has been successfully used to simulate steady flow around complete aircraft configurations [8], led naturally to schemes which can achieve second order accuracy in smooth flows without introducing spurious numerical oscillations in the vicinity of discontinuities. Those schemes, however, reduce to first order accuracy away from the steady state, so much recent research has aimed to impose the same combination of properties on time-dependent simulations, leading to the space-time formulation [5] described briefly in Section 2.…”

Section: Introductionmentioning

confidence: 99%

Discontinuous fluctuation distribution

Hubbard

2008

Journal of Computational Physics

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This paper proposes an approach to the approximation of timedependent hyperbolic conservation laws which is both second order accurate in space and time (for any sufficiently smooth solution profile, even one containing turning points) and free of spurious oscillations for any time-step. The numerical algorithm is based on the concept of fluctuation distribution, applied on a space-time mesh of triangular prisms, for which second order accurate schemes already exist which are oscillation-free if the time-step satisfies a CFL-type constraint. This restriction is lifted here by combining the concept of a two-layer scheme with a representation of the solution which is allowed to be discontinuous in time. Numerical results are presented in two space dimensions, using unstructured meshes of space-time triangular prisms, for the scalar advection equation, Burgers' equation and the Euler equations of gasdynamics.Key-words: conservation laws, positivity, stability, large time steps, residual distribution, second order accuracy * University of Leeds † INRIA Bordeaux -Sud-Ouest Discontinuous residual distribution : A route to unconditional positivity and high order accuracyRésumé : This paper proposes an approach to the approximation of timedependent hyperbolic conservation laws which is both second order accurate in space and time (for any sufficiently smooth solution profile, even one containing turning points) and free of spurious oscillations for any time-step. The numerical algorithm is based on the concept of fluctuation distribution, applied on a space-time mesh of triangular prisms, for which second order accurate schemes already exist which are oscillation-free if the time-step satisfies a CFL-type constraint. This restriction is lifted here by combining the concept of a two-layer scheme with a representation of the solution which is allowed to be discontinuous in time. Numerical results are presented in two space dimensions, using unstructured meshes of space-time triangular prisms, for the scalar advection equation, Burgers' equation and the Euler equations of gasdynamics.

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Status of multidimensional upwind residual distribution schemes and applications in aeronautics

Cited by 54 publications

References 14 publications

An ALE Formulation for Explicit Runge-Kutta Residual Distribution

An ALE Formulation for Explicit Runge-Kutta Residual Distribution

Parallel anisotropic mesh refinement with dynamic load balancing for transonic flow simulations

Discontinuous fluctuation distribution

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