The behavior of flux difference splitting schemes near slowly moving shock waves

Roberts, Thomas W.

doi:10.1016/0021-9991(90)90200-k

Cited by 100 publications

(62 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Unfortunately, Roberts has shown that the nature of the shock structure produced by a particular scheme can have a large bearing on how well the scheme copes with slowly moving shock waves [21]. Godunov-type methods fare quite badly in this respect, as the shock moves relative to the mesh, the shock profile flexes, perturbing the supposedly passive characteristic fields as it does so.…”

Section: Slowly Moving Shocksmentioning

confidence: 99%

A contribution to the great Riemann solver debate

Quirk

1994

Numerical Methods in Fluids

674

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

Section: Slowly Moving Shocksmentioning

confidence: 99%

A contribution to the great Riemann solver debate

Quirk

1994

Numerical Methods in Fluids

674

524

View full text Add to dashboard Cite

show abstract

“…In order to test other types of problems, we have run our method on the slow shock proposed in [13]. Again, an overshoot appears, which is immediately damped while an oscillation usually propagates with first-order solvers [13].…”

Section: Minimal Limitations For Second-order Schemesmentioning

confidence: 99%

“…Again, an overshoot appears, which is immediately damped while an oscillation usually propagates with first-order solvers [13]. We have also tested the shock tube proposed by Einfeldt, Munz, Roe, and Sjögreen of [14] [14], where a zero temperature point arises.…”

Section: Minimal Limitations For Second-order Schemesmentioning

confidence: 99%

Maximum Principle on the Entropy and Second-Order Kinetic Schemes

Khobalatte¹,

Perthame²

1994

Mathematics of Computation

View full text Add to dashboard Cite

Abstract.We consider kinetic schemes for the multidimensional inviscid gas dynamics equations (compressible Euler equations). We prove that the discrete maximum principle holds for the specific entropy. This fixes the choice of the equilibrium functions necessary for kinetic schemes. We use this property to perform a second-order oscillation-free scheme, where only one slope limitation (for three conserved quantities in 1D) is necessary. Numerical results exhibit stability and strong convergence of the scheme.

show abstract

“…In [1,17,16] and references therein, it has been observed that the numerical computation of slowly moving shock waves displays an anomalous behavior inherent to nonlinear systems: the numerical values in the postshock region display an oscillatory behavior which is completely nonphysical. Numerical results computed by the present, Marquina, and HLLE schemes are displayed in Fig.…”

Section: One-dimensional Testsmentioning

confidence: 99%

“…In our first-order scheme, the noise is undetectable, but the shock layer is less sharp than in the HLLE scheme. It was observed in [17] that this pathological behavior is worse when using high-order versions of numerical schemes. This is clearly appreciated in the PHM-HLLE scheme.…”

Section: One-dimensional Testsmentioning

confidence: 99%

A Nonlinear Flux Split Method for Hyperbolic Conservation Laws

Stiriba¹

2002

Journal of Computational Physics

View full text Add to dashboard Cite

We present and analyze the performance of a nonlinear, upwind flux split method for approximating solutions of hyperbolic conservation laws. The method is based on a new version of the single-state-approximate Riemann solver devised by Harten, Lax, and van Leer (HLL) and implemented by Einfeldt. It makes use of two-sided local characteristic variables to reduce the dissipation of HLL by introducing the flavor of HLL into the Steger-Warming flux vector splitting scheme. We use the characteristic decomposition and the method-of-lines approach to construct high-order versions of the first-order scheme and demonstrate their efficiency and robustness in several numerical tests.

show abstract

The behavior of flux difference splitting schemes near slowly moving shock waves

Cited by 100 publications

References 6 publications

A contribution to the great Riemann solver debate

A contribution to the great Riemann solver debate

Maximum Principle on the Entropy and Second-Order Kinetic Schemes

A Nonlinear Flux Split Method for Hyperbolic Conservation Laws

Contact Info

Product

Resources

About