A high-order accurate unstructured finite volume Newton–Krylov algorithm for inviscid compressible flows

Nejat, Amir; Ollivier‐Gooch, Carl

doi:10.1016/j.jcp.2007.11.011

Cited by 79 publications

(71 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The computation of stationary solutions to hyperbolic equations is rarely performed with implicit solvers. Their development has been pursued by several groups [10][11][12][13] for the Euler equations. However, many existing schemes employ linearizable/differentiable limiters, are conditionally stable, and the rate of steady-state convergence deteriorates if the CFL number exceeds a certain upper bound.…”

Section: Introductionmentioning

confidence: 99%

Implicit finite element schemes for stationary compressible particle-laden gas flows

Gurris

Kuzmin

Turek

2011

Journal of Computational and Applied Mathematics

View full text Add to dashboard Cite

a b s t r a c tThe derivation of macroscopic models for particle-laden gas flows is reviewed. Semiimplicit and Newton-like finite element methods are developed for the stationary two-fluid model governing compressible particle-laden gas flows. The Galerkin discretization of the inviscid fluxes is potentially oscillatory and unstable. To suppress numerical oscillations, the spatial discretization is performed by a high-resolution finite element scheme based on algebraic flux correction. A multidimensional limiter of TVD type is employed. An important goal is the efficient computation of stationary solutions in a wide range of Mach numbers. This is a challenging task due to oscillatory correction factors associated with TVD-type flux limiters and the additional strong nonlinearity caused by interfacial coupling terms. A semi-implicit scheme is derived by a time-lagged linearization of the nonlinear residual, and a Newton-like method is obtained in the limit of infinite CFL numbers. The original Jacobian is replaced by a low-order approximation. Special emphasis is laid on the numerical treatment of weakly imposed boundary conditions. It is shown that the proposed approach offers unconditional stability and faster convergence rates for increasing CFL numbers. The strongly coupled solver is compared to operator splitting techniques, which are shown to be less robust.

show abstract

Section: Introductionmentioning

confidence: 99%

Implicit finite element schemes for stationary compressible particle-laden gas flows

Gurris

Kuzmin

Turek

2011

Journal of Computational and Applied Mathematics

View full text Add to dashboard Cite

show abstract

“…Of course, shocks and vortices still require an adequate local mesh to catch all the structures but high-order schemes prove to be efficient in reducing the numerical diffusion. For instance the k-exact reconstruction [3,4,34] increases the method accuracy using quadratic or cubic polynomial approximations [32,35,36]. Nevertheless, traditional TVD (Total Variation Diminishing) limiting procedures drastically reduce the order of accuracy despite the construction of alternative limiters [45,33] to enhance the quality of the solution.…”

mentioning

confidence: 99%

a posteriori stabilized sixth-order finite volume scheme for one-dimensional steady-state hyperbolic equations

2017

View full text Add to dashboard Cite

To cite this version:Stéphane Clain, Raphaël Loubère, Gaspar Machado. a posteriori stabilized sixth-order finite volume scheme for one-dimensional steady-state hyperbolic equations. 2016. a posteriori stabilized sixth-order finite volume scheme for one-dimensional steady-state hyperbolic equationsWe propose a new family of finite volume high-accurate numerical schemes devoted to solve one-dimensional steady-state hyperbolic systems. High-accuracy (up to the sixth-order presently) is achieved thanks to polynomial reconstructions while stability is provided with an a posteriori MOOD method which control the cell polynomial degree for eliminating non-physical oscillations in the vicinity of discontinuities. Such a procedure demands the determination of a chain detector to discriminate between troubled and valid cells, a cascade of polynomial degrees to be successively tested when oscillations are detected, and a parachute scheme corresponding to the last, viscous, and robust scheme of the cascade. Experimented on linear, Burgers', and Euler equations, we demonstrate that the schemes manage to retrieve smooth solutions with optimal order of accuracy but also irregular solutions without spurious oscillations.

show abstract

“…Identifying a suitable collection of cells from the original block and its neighbors is therefore not trivial. In the fully unstructured and "mesh-free" computational-fluid-dynamics literature, one technique for reconstruction is least-squares interpolation [3,4,24,15,27,23,19,8], which does not presume any underlying spatial relationship between the values used in the interpolation. This is the approach we take here.…”

Section: Major Radiusmentioning

confidence: 99%

High-order finite-volume methods for hyperbolic conservation laws on mapped multiblock grids

McCorquodale

Dorr

Hittinger

et al. 2015

Journal of Computational Physics

View full text Add to dashboard Cite

We present an approach to solving hyperbolic conservation laws by finitevolume methods on mapped multiblock grids, extending the approach of Colella, Dorr, Hittinger, and Martin (2011) for grids with a single mapping. We consider mapped multiblock domains for mappings that are conforming at inter-block boundaries. By using a smooth continuation of the mapping into ghost cells surrounding a block, we reduce the inter-block communication problem to finding an accurate, robust interpolation into these ghost cells from neighboring blocks. We demonstrate fourth-order accuracy for the advection equation for multiblock coordinate systems in two and three dimensions.

show abstract

A high-order accurate unstructured finite volume Newton–Krylov algorithm for inviscid compressible flows

Cited by 79 publications

References 41 publications

Implicit finite element schemes for stationary compressible particle-laden gas flows

Implicit finite element schemes for stationary compressible particle-laden gas flows

a posteriori stabilized sixth-order finite volume scheme for one-dimensional steady-state hyperbolic equations

High-order finite-volume methods for hyperbolic conservation laws on mapped multiblock grids

Contact Info

Product

Resources

About