A second-order-accurate monotone implicit fluctuation splitting scheme for unsteady problems

Palma, P. De; Pascazio, G.; Rossiello, Gaetano; Napolitano, M.

doi:10.1016/j.jcp.2004.11.023

Cited by 29 publications

(35 citation statements)

References 19 publications

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“…This leads to implicit schemes, even if the spatial residual were treated explicitly. Although a more general framework for the derivation of the mass matrices can be devised [10], the approach adopted in our study consists of formulating the FS scheme as a Petrov-Galerkin FE method with elemental weighting function given by…”

Section: Time 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: Time 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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“…For this reason, time dependent implementations of RD always feature some form of implicit time integration [12,13,14,32,33], or a fully coupled space-time formulation [17,34,35]. Moreover, positivity preservation always requires the satisfaction of time step constraints [36,14], unless some form of nonlinear time (or space-time) discretization is used [37,34,35].…”

Section: Genuinely Explicit Rk-rd Time Marching Proceduresmentioning

confidence: 99%

An ALE Formulation for Explicit Runge–Kutta Residual Distribution

2014

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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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“…The Space-Time residual distribution framework [5,15,17,22,34] is very faithful to the RD and multidimensional upwinding spirit. Although it allows construction of discretisations with all the desired properties, those methods are subject to a CFL-type restriction on the time-step.…”

Section: Introductionmentioning

confidence: 99%

“…This approach was implemented and investigated in a number of references, i.e. [5,18,33,34] or [11]. In all of these references the authors used multi-step methods to integrate the underlying PDE in time.…”

Section: Introductionmentioning

confidence: 99%

Runge–Kutta Residual Distribution Schemes

2014

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We are concerned with the solution of time-dependent non-linear hyperbolic partial differential equations. We investigate the combination of residual distribution methods with a consistent mass matrix (discretisation in space) and a Runge-Kutta-type time-stepping (discretisation in time). The introduced non-linear blending procedure allows us to retain the explicit character of the time-stepping procedure. The resulting methods are second order accurate provided that both spatial and temporal approximations are. The proposed approach results in a global linear system that has to be solved at each time-step. An efficient way of solving this system is also proposed. To test and validate this new framework, we perform extensive numerical experiments on a wide variety of classical problems. An extensive numerical comparison of our approach with other multi-stage residual distribution schemes is also given.

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A second-order-accurate monotone implicit fluctuation splitting scheme for unsteady problems

Cited by 29 publications

References 19 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

An ALE Formulation for Explicit Runge–Kutta Residual Distribution

Runge–Kutta Residual Distribution Schemes

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