Numerical (error) issues on compressible multicomponent flows using a high-order differencing scheme: Weighted compact nonlinear scheme

Nonomura, Taku; Morizawa, Seiichiro; Terashima, Hiroshi; Obayashi, Shigeru; Fujii, Kozo

doi:10.1016/j.jcp.2011.12.035

Cited by 63 publications

(36 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The next case was the two-dimensional compressible multi-material Richtmyer-Meshkov instability problem [32]. The heavy and light fluids were SF 6 and air, respectively.…”

Section: Two-dimensional Richtmyer-meshkov Instabilitymentioning

confidence: 99%

“…The final test was the two-dimensional shock-bubble interaction problem [32]. A schematic of the initial flow configuration is shown in Fig.…”

Section: Shock-bubble Interaction Problemmentioning

confidence: 99%

“…They analyzed the numerical oscillations and suggested that only the reconstruction of primitive variables can eliminate the spurious oscillations because the specific heat ratio is not constant [31]. Nonomura et al [32] more comprehensively discussed the numerical oscillations of compressible multi-material flows and concluded that primitive variable interpolation can effectively eliminate numerical oscillations and that a better choice of fully conservative or quasi-conservative forms depends on the problem. Here, we emphasize that Nonomura et al selected the weighted-compact-nonlinear-scheme (WCNS) variable interpolation finite difference formulation [33] to take over the numerical technique developed with the FVM [19].…”

Section: Introductionmentioning

confidence: 99%

“…As argued by Nonomura et al [32], the technique proposed by Johnsen and Colonius [19] cannot be applied to the finite difference WENO schemes because these schemes do not include primitive variable reconstruction. In this paper, we present a systematic analysis of this question.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Preventing numerical oscillations in the flux-split based finite difference method for compressible flows with discontinuities

Zhang

et al. 2015

Journal of Computational Physics

View full text Add to dashboard Cite

In simulating compressible flows with contact discontinuities or material interfaces, numerical pressure and velocity oscillations can be induced by point-wise flux vector splitting (FVS) or component-wise nonlinear difference discretization of convection terms. The current analysis showed that the oscillations are due to the incompatibility of the point-wise splitting of eigenvalues in FVS and the inconsistency of component-wise nonlinear difference discretization among equations of mass, momentum, energy, and even fluid composition for multi-material flows. Two practical principles are proposed to prevent these oscillations: (i) convective fluxes must be split by a global FVS, such as the global Lax-Friedrichs FVS, and (ii) consistent discretization between different equations must be guaranteed. The latter, however, is not compatible with component-wise nonlinear difference discretization. Therefore, a consistent discretization method that uses only one set of common weights is proposed for nonlinear weighted essentially non-oscillatory (WENO) schemes. One possible procedure to determine the common weights is presented that provided good results. The analysis and methods stated above are appropriate for both single-(e.g., contact discontinuity) and multi-material (e.g., material interface) discontinuities. For the latter, however, the additional fluid composition equation should be split and discretized consistently for compatibility with the other equations. Numerical tests including several contact discontinuities and multi-material flows confirmed the effectiveness, robustness, and low computation cost of the proposed method.

show abstract

“…The next case was the two-dimensional compressible multi-material Richtmyer-Meshkov instability problem [32]. The heavy and light fluids were SF 6 and air, respectively.…”

Section: Two-dimensional Richtmyer-meshkov Instabilitymentioning

confidence: 99%

“…The final test was the two-dimensional shock-bubble interaction problem [32]. A schematic of the initial flow configuration is shown in Fig.…”

Section: Shock-bubble Interaction Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Preventing numerical oscillations in the flux-split based finite difference method for compressible flows with discontinuities

Zhang

et al. 2015

Journal of Computational Physics

View full text Add to dashboard Cite

show abstract

“…In the case of computation of multiple-gas-component modeling, the mass-fraction equation is solved with the conservative form which generates spurious numerical errors, but we try to minimize the error using the primitive variable interpolation. 14) In this framework, we can conserve the mass of different species with minimum error. With regard to the turbulence modeling, the explicit subgrid model is not used, thus the modeling of the present computation is categorized into monotonically integrated large eddy simulation (MILES).…”

Section: Methodsmentioning

confidence: 99%

Computational Prediction of Acoustic Waves from a Subscale Rocket Motor

Nonomura

Morizawa

Obayashi

et al. 2014

AEROSPACE TECHNOLOGY JAPAN

Self Cite

View full text Add to dashboard Cite

For improvement of prediction of acoustics waves from a rocket plume, validation studies of numerical simulation are performed using experimental data of acoustics waves from subscale rocket motors, and prediction accuracy of numerical simulation is discussed. Experimental data of flow and acoustics fields of a solid motor and a H2-AIR liquid motor are used as the reference. The computational results of the far-field OASPL agree with experimental data within the error of approximately 5dB. The result shows that the current numerical methods well predict Mach waves at downstream side even though the results of far-field PSD are slightly overestimated. Meanwhile, it is difficult to capture shock associated acoustic waves and fine-scale turbulence acoustic waves at upstream side and the results of far-field PSD are underestimated. In addition, difference between single and multicomponent in the computational results is also small.

show abstract

Preventing numerical oscillations in the flux‐split based finite difference method for compressible flows with discontinuities, II

Zhang

et al. 2015

Numerical Methods in Fluids

View full text Add to dashboard Cite

SUMMARYProblems in the characteristic-wise flux-split based finite difference method when compressible flows with contact discontinuities or material interfaces are computed were presented and analyzed. The current analysis showed the following: (i) Even with the local characteristic decomposition technique, numerical errors could be caused by point-wise flux vector splitting (FVS) methods, such as the Steger-Warming FVS or the van Leer FVS. Therefore, the Lax-Friedrichs type FVS method is required. (ii) If the isobars of a material are vertical lines, the combination of using the local characteristic decomposition and the global LaxFriedrichs FVS can avoid velocity and pressure oscillations of contact discontinuities in this material for weighted essentially non-oscillatory (WENO) schemes. (iii) For problems with material interfaces, the quasiconservative approach can be realized using characteristic-wise flux-split based finite difference WENO schemes if nonlinear WENO schemes in genuinely nonlinear characteristic fields can be guaranteed to be the same and the decomposition equation representing material interfaces is discretized properly. Copyright

show abstract

Numerical (error) issues on compressible multicomponent flows using a high-order differencing scheme: Weighted compact nonlinear scheme

Cited by 63 publications

References 31 publications

Preventing numerical oscillations in the flux-split based finite difference method for compressible flows with discontinuities

Preventing numerical oscillations in the flux-split based finite difference method for compressible flows with discontinuities

Computational Prediction of Acoustic Waves from a Subscale Rocket Motor

Preventing numerical oscillations in the flux‐split based finite difference method for compressible flows with discontinuities, II

Contact Info

Product

Resources

About