Normalized Variable and Space Formulation Methodology for High-Resolution Schemes

Darwish, M.; Moukalled, F.

doi:10.1080/10407799408914918

Cited by 129 publications

(85 citation statements)

References 18 publications

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“…In this work we selected the popular MINMOD [10] and SMART [8] schemes, which are expressed in the NVSF as [4]: and are illustrated in Fig. 3 in the NVD.…”

Section: High-resolution Schemesmentioning

confidence: 99%

“…(1) deserves special treatment, as described in Section 1. For the implementation of high-resolution schemes we follow the NVSF of Darwish and Moukalled [4], which is an extension to non-uniform grids of the NVF of Leonard [20,21]. In the NVSF approach, the convection flux F and the co-ordinate x are normalized as…”

Section: High-resolution Schemesmentioning

confidence: 99%

“…Several discretization schemes were proposed on the total variation diminishing framework (TVD) [10,27], and more recently on the normalized variable formulation (NVF) [20] and its extension, the normalized variable and space formulation (NVSF) of Darwish and Moukalled [4], to be described below.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Adaptive multiresolution approach for solution of hyperbolic PDEs

Alves

Cruz

Mendes

et al. 2002

Computer Methods in Applied Mechanics and Engineering

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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.

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“…In this work we selected the popular MINMOD [10] and SMART [8] schemes, which are expressed in the NVSF as [4]: and are illustrated in Fig. 3 in the NVD.…”

Section: High-resolution Schemesmentioning

confidence: 99%

Section: High-resolution Schemesmentioning

confidence: 99%

See 1 more Smart Citation

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

“…Therefore, the presented algorithm can be included in the class of h-refinement (static regridding) PDE solution adaptive procedures. The finite difference coefficients are computed using the recursive method of Fornberg (Fornberg, 1988), the HRS schemes are based on the NVSF method (Darwish and Moukalled, 1994) associated to flux limiting strategies, such as SMART or MINMOD procedures , and the interpolation step is done by linear or cubic splines approximations.…”

Section: Algorithmmentioning

confidence: 99%

1D AND 2D MODELING AND SIMULATION OF RADIAL COMBUSTION PROPAGATION ON Fe2O3/Al THERMITE SYSTEMS

Brito

Durães

Portugal

2012

Comput Thermal Scien

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In previous works, a one-dimensional model was built to simulate the nonsteady radial combustion propagation on thin disk-shaped samples of Fe2O3/aluminum thermite mixtures and was successfully tested. Now, the purpose is to extend the referred model to the more sensible two-dimensional features of the samples, maintaining the main characteristics of the previous model: zero-order kinetics, conductive/radiative heat transfer, assumption of phase transitions, temperature and composition dependency for all system properties during propagation. Therefore, an adaptive numerical algorithm that conjugates a method of lines (MOL) strategy based on finite differences space discretizations, with a collocation scheme based on increasing level dyadic grids is applied for the solution of the problem. The particular integration method proves to cope satisfactorily with the steep traveling thermal wave in 1D and 2D spatial domains, either for trivial uniform mixing conditions, as in complex examples developed to feature more sophisticated circumstances, such as nonhomogeneous reactant mixing, which realistically replicate the observed experimental conditions.

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“…When a first order scheme is used, the variables at a given face of the CV are taken equal to the nearest upstream nodal values (this is the upwind scheme). Higher order schemes, as Quick or Smart [15], are introduced using a deferred correction approach, i.e. the convective term is evaluated using the upwind scheme while an extra or correction term is introduced in the source term of the discretized equation keeping the diagonal dominance of the coefficient matrix.…”

Section: Energy Equationmentioning

confidence: 99%