High-order accurate, low numerical diffusion methods for aerodynamics

Ekaterinaris, John A.

doi:10.1016/j.paerosci.2005.03.003

Cited by 232 publications

(106 citation statements)

References 228 publications

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“…The flux vector F can be computed at any point (x, y, z) by the following 9) where N s is the number of nodes in the nodal set, calculated from (2.2), F i is the flux vector evaluated at node i , and M i (x,y,z) are the shape functions defined by the nodal set which satisfy…”

Section: Review Of the Quadrature-free Spectral Volume Methodsmentioning

confidence: 99%

Final Report - High-Order Spectral Volume Method for the Navier-Stokes Equations On Unstructured Tetrahedral Grids

Wang¹

2012

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Section: Review Of the Quadrature-free Spectral Volume Methodsmentioning

confidence: 99%

Final Report - High-Order Spectral Volume Method for the Navier-Stokes Equations On Unstructured Tetrahedral Grids

Wang¹

2012

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“…The extensive use of Computational Fluid Dynamics (CFD) in numerous engineering applications leads to many fundamental questions regarding the applied numerical approaches themselves, especially the effects of the numerical schemes on the simulation results, which have been investigated in many studies, as for examples [1][2][3][4]. Obviously, reducing the numerical errors is essential for an accurate solution of the transport equations of different physical quantities [5,6].…”

Section: Introductionmentioning

confidence: 99%

Investigation of Numerical Effects on the Flow and Combustion in LES of ICE

Nguyen

Kempf

2017

Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles

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-This work investigates the influence of numerical dissipation on the modeled combustion in Large Eddy Simulations (LES). It is well known that capturing the dynamics of the in-cylinder flow is crucial for engine simulations, as it strongly affects flame propagation. The flame propagation during the power-stroke highly depends on the turbulence level that is developed throughout compression. This turbulence level will be strongly influenced by the accuracy of the numerical schemes employed. Even a small extent of upwinding, filtering, low-order implicit time-stepping, cell-stretching or mapping between grids may affect the flow field, the turbulence level, and hence the turbulent flame speed and the pressure curve. To provide a reference, the LES in-house code PsiPhi is used, which ensures a minimum of dissipation due to high order explicit time-stepping, homogeneous and isotropic filters and cells. Good stability of the code permits the use of a second-order Central Differencing Scheme (CDS) for the transport of momentum, avoiding numerical dissipation. To analyse the effect of numerical dissipation, simulations of a fired engine are performed using different numerical schemes for the convection of momentum. Physical quantities including the total kinetic energy, the velocity gradient, the turbulent viscosity, the in-cylinder pressure, the flame propagation or the burning rate of different test cases are evaluated and compared to each other to show the numerical effects on combustion. Furthermore, the suitability of common LES quality criteria including an energy criterion and viscosity ratio is discussed based on the comparison of simulations with less and more accurate numerics. It is shown that these LES quality indicators can be highly misleading.

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“…In fact, there are many high-order numerical methods [8,9] developed in the past decades: the essentially non-oscillatory method (ENO) [10], the weighted ENO (WENO) method [11,12], the discontinuous Galerkin method [13], and the spectral volume method [14]. In this article, the WENO method is employed.…”

Section: Introductionmentioning

confidence: 99%

An improved unstructured WENO method for compressible multi‐fluids flow

Zheng

Zhao

2016

Numerical Methods in Fluids

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SUMMARYAn improved high-order accurate WENO finite volume method based on unstructured grids for compressible multi-fluids flow is proposed in this paper. The third-order accuracy WENO finite volume method based on triangle cell is used to discretize the governing equations. To have higher order of accuracy, the P1 polynomial is reconstructed firstly. After that, the P2 polynomial is reconstructed from the combination of the P1. The reconstructed coefficients are calculated by analytical form of inverse matrix rather than the numerical inversion. This greatly improved the efficiency and the robustness. Four examples are presented to examine this algorithm. Numerical results show that there is no spurious oscillation of velocity and pressure across the interface and high-order accurate result can be achieved.

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High-order accurate, low numerical diffusion methods for aerodynamics

Cited by 232 publications

References 228 publications

Final Report - High-Order Spectral Volume Method for the Navier-Stokes Equations On Unstructured Tetrahedral Grids

Final Report - High-Order Spectral Volume Method for the Navier-Stokes Equations On Unstructured Tetrahedral Grids

Investigation of Numerical Effects on the Flow and Combustion in LES of ICE

An improved unstructured WENO method for compressible multi‐fluids flow

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