A contribution to the numerical prediction of unsteady flows

Pandolfi, Maurizio

doi:10.2514/6.1983-121

Cited by 13 publications

(19 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The solution is also the same for FDSROE (since the approximate solver proposed in [19] becomes exact if small initial discontinuities define the RP) and for FDSPAN [16] and for the method proposed in [15] (because the only approximation in these two solvers is introduced in the case of intense shock waves).…”

Section: Moc Fdsroe and Fdspanmentioning

confidence: 79%

“…However, to save computing time, approximate solvers of the RP have been proposed. Among these, mention should be made of the one suggested in [19] (FDSROE), an exact solver of a linearized definition of the RP, the one suggested in [15], which is an approximate solution of the actual RP, and the mirror image of the latter proposed in [16] (FDSPAN).…”

Section: Upwind Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Numerical Instabilities in Upwind Methods: Analysis and Cures for the “Carbuncle” Phenomenon

Pandolfi¹,

D’Ambrosio²

2001

Journal of Computational Physics

289

215

View full text Add to dashboard Cite

Section: Moc Fdsroe and Fdspanmentioning

confidence: 79%

Section: Upwind Methodsmentioning

confidence: 99%

Numerical Instabilities in Upwind Methods: Analysis and Cures for the “Carbuncle” Phenomenon

Pandolfi¹,

D’Ambrosio²

2001

Journal of Computational Physics

289

215

View full text Add to dashboard Cite

“…His motivation being, that approximate solutions can be computed much more cheaply than exact solutions. Thus the industry of designing approximate Riemann solvers was born [14,15,4,23]. Now whilst Godunov-type schemes are often held up to be models of robustness they can on occasions fail quite spectacularly.…”

Section: Introductionmentioning

confidence: 99%

A contribution to the great Riemann solver debate

Quirk

1994

Numerical Methods in Fluids

681

524

View full text Add to dashboard Cite

The aims of this paper are threefold: to increase the level of awareness within the shock‐capturing community of the fact that many Godunov‐type methods contain subtle flaws that can cause spurious solutions to be computed; to identify one mechanism that might thwart attempts to produce very‐high‐resolution simulations; and to proffer a simple strategy for overcoming the specific failings of individual Riemann solvers.

show abstract

“…xi; 1 2 4x u n (x)dx: (9) Furthermore, u n may denote the discrete numerical solution at time level t n , u n (x) o r u(x t n ). u n L and u n R are the numerical approximations of u L (t n ) a n d u R (t n ), respectively.…”

Section: The Problemmentioning

confidence: 99%

Error estimators for the position of discontinuities in hyperbolic conservation laws with source terms which are solved using operator splitting

Jeltsch

Klingenstein

1999

Computing and Visualization in Science

View full text Add to dashboard Cite

When computing numerical solutions of hyperbolic conservation laws with source terms, one may obtain spurious solutions | these are unphysical solutions that only occur in numerics such a s s h o c k w aves moving with wrong speeds, cf. 7], 2], 1], 10], 3]. Therefore it is important to know h o w errors of the location of a discontinuity can be controlled.To d e r i v e appropriate error-estimates and to use them to control such errors, is the aim of our investigations in this paper. We restrict our considerations t o numerical solutions which are computed by using a splitting method. In splitting methods, the homogeneous conservation law and an ordinary di erential equation (modelling the source term) are solved separately in each t i m e s t e p .Firstly, w e d e r i v e error-estimates for the scalar Riemann problem. The analysis shows that the local error of the location of a discontinuity mainly consists of two parts. The rst part is introduced by the splitting and the second part is due to smearing of the discontinuity.Next, these error-estimates are used to construct an adaptation of the step size so that the error of the location of the discontinuity remains su ciently small. The adaptation is applied to several examples, which are a scalar problem, a simpli ed combustion model, and the one-dimensional i n viscid reacting compressible Euler equations. All the examples show that the adaptation based on the derived error-estimates works well.The theory can also be extended to planar two-dimensional problems.

show abstract

A contribution to the numerical prediction of unsteady flows

Cited by 13 publications

References 4 publications

Numerical Instabilities in Upwind Methods: Analysis and Cures for the “Carbuncle” Phenomenon

Numerical Instabilities in Upwind Methods: Analysis and Cures for the “Carbuncle” Phenomenon

A contribution to the great Riemann solver debate

Error estimators for the position of discontinuities in hyperbolic conservation laws with source terms which are solved using operator splitting

Contact Info

Product

Resources

About