On a higher-order bounded discretization scheme

Song, Bin; Liu, G. R.; Lam, K.Y.; Amano, Ryoichi S.

doi:10.1002/(sici)1097-0363(20000415)32:7<881::aid-fld2>3.0.co;2-6

Cited by 66 publications

(58 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…This semi-discrete central scheme requires the use of a TVD limiter. It is not difficult to modify the SMART scheme so that the resulting piecewise linear formulation in NVSF satisfies TVD constraints, and a recent proposal in that direction was put forth by Song et al [26], the WACEB high-resolution scheme. In this scheme a normalized face flux is calculated from the expression:…”

Section: Euler System Of Equationsmentioning

confidence: 99%

Adaptive multiresolution approach for solution of hyperbolic PDEs

Alves

Cruz

Mendes

et al. 2002

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

This paper establishes an innovative and efficient multiresolution adaptive approach combined with high-resolution methods, for the numerical solution of a single or a system of partial differential equations. The proposed methodology is unconditionally bounded (even for hyperbolic equations) and dynamically adapts the grid so that higher spatial resolution is automatically allocated to domain regions where strong gradients are observed, thus possessing the two desired properties of a numerical approach: stability and accuracy.Numerical results for five test problems are presented which clearly show the robustness and cost effectiveness of the proposed method.

show abstract

Section: Euler System Of Equationsmentioning

confidence: 99%

Adaptive multiresolution approach for solution of hyperbolic PDEs

Alves

Cruz

Mendes

et al. 2002

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

show abstract

“…The uncertainty in the results is of the order of 0.1% for mesh M3 and of 0.2% for mesh M2. These results also show that the Table III also contains X R and Y R data for Re = 400 and = 0.5 using CDS and CUBISTA, as well as the high-resolution schemes SMART of Gaskell and Lau [47] and WACEB of Song et al [48] used to help confirm the results obtained with the CUBISTA scheme. For X R the predictions of CUBISTA and CDS already agree for mesh M3 to within 0.1%, whereas for Y R CDS is taking longer than CUBISTA to converge to a mesh-independent value.…”

Section: Steady Laminar Diverging Flow Of Newtonian Fluids In a 90mentioning

confidence: 99%

Steady and unsteady laminar flows of Newtonian and generalized Newtonian fluids in a planar T‐junction

Miranda

Oliveira

Pinho

2007

Numerical Methods in Fluids

View full text Add to dashboard Cite

SUMMARYAn investigation of laminar steady and unsteady flows in a two-dimensional T-junction was carried out for Newtonian and a non-Newtonian fluid analogue to blood. The flow conditions considered are of relevance to hemodynamical applications and the localization of coronary diseases, and the main objective was to quantify the accuracy of the predictions and to provide benchmark data that are missing for this prototypical geometry. Under steady flow, calculations were performed for a wide range of Reynolds numbers and extraction flow rate ratios, and accurate data for the recirculation sizes were obtained and are tabulated. The two recirculation zones increased with Reynolds number, but the behaviour was non-monotonic with the flow rate ratio. For the pulsating flows a periodic instability was found, which manifests itself by the breakdown of the main vortex into two pieces and the subsequent advection of one of them, while the secondary vortex in the main duct was absent for a sixth of the oscillating period. Shear stress maxima were found on the walls opposite the recirculations, where the main fluid streams impinge onto the walls. For the blood analogue fluid, the recirculations were found to be 10% longer but also short lived than the corresponding Newtonian eddies, and the wall shear stresses are also significantly different especially in the branch duct.

show abstract

“…Usando as ferramentas NVD e TVD, Song e seu colaboradores [67] propuseram o esquema WACEB ("Weighted-Average Coefficient Ensuring Boundedness"), que pode atingir terceira ordem e é limitado. Testes numéricos em geometrias específicas demonstraram que este esquema tem a habilidade do esquema QUICK em reduzir a difusão numérica sem introduzir oscilação na solução.…”

Section: Um Breve Histórico De Esquemas "Upwind"unclassified

“…Um esquema recente proposto Song et al [67] (veja também [43]) para a resolução de problemas estacionários é o esquema WACEB, que é limitado e pode alcançar a terceira-ordem de precisão do QUICK. O fluxo numérico, em variáveis normalizadas, desse esquema é dado por…”

Section: Caso Estacionáriounclassified

Modelagem Matemática e Simulação Numérica em Dinâmica dos Fluidos.

2005

Notas Em Matemática Aplicada

View full text Add to dashboard Cite

On a higher-order bounded discretization scheme

Cited by 66 publications

References 11 publications

Adaptive multiresolution approach for solution of hyperbolic PDEs

Adaptive multiresolution approach for solution of hyperbolic PDEs

Steady and unsteady laminar flows of Newtonian and generalized Newtonian fluids in a planar T‐junction

Modelagem Matemática e Simulação Numérica em Dinâmica dos Fluidos.

Contact Info

Product

Resources

About