Comparison of structured- and unstructured-grid, compressible and incompressible methods using the vortex pairing problem

Abstract

The accuracy, robustness, dissipation characteristics and efficiency of several structured and unstructured grid methods are investigated with reference to the low Mach double vortex pairing flow problem. The aim of the study is to shed light into the numerical advantages and disadvantages of different numerical discretizations, principally designed for shock-capturing, in low Mach vortical flows. The methods include structured and unstructured finite volume and Lagrange-Remap methods, with accuracy ranging from 2nd to 9th-order, with and without applying low-Mach corrections. Comparison of the schemes is presented for the vortex evolution, momentum thickness, as well as for their numerical dissipation versus the viscous and total dissipation. The study shows that the momentum thickness and large scale features of a basic vortical structure are well resolved even at the lowest grid resolution of 32×32 provided that the numerical schemes are of a high-order of accuracy or the numerical framework is sufficiently non-dissipative. The implementation of the finite volume methods in unstructured triangular meshes provides the best results even without low Mach number corrections provided that a higher-order advective discretization for the advective fluxes is employed. The compressible Lagrange-Remap framework is computationally the fastest one, although the numerical error for the momentum thickness does not reduce as fast as for other numerical schemes and computational frameworks, e.g., when higher-order schemes are utilized. It is also shown that the low-Mach number correction has a lesser effect on the results as the order of the spatial accuracy increases

Assessment of high-order finite volume methods on unstructured meshes for RANS solutions of aeronautical configurations

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“…The diagonal elements of the matrix must be stored and inverted directly and the off-diagonal ones are computed at every stage. Hence, the diagonal elements used in the present study are scalars multiplied by the identity matrix and the off-diagonals are computed according to equation (33). The number of sweeps per Newton iteration is set to 5 in the present study, based on the findings of various approaches using the LU-SGS schemes for similar flow problems [56][57][58][59][60][61].…”

“…Furthermore, low Mach number effects can become important in near wall regions as well as in flow regions where vortical structures are 2 dominant [32,33]. Numerical methods designed for compressible flows should be assessed for their accuracy in these flow regions.…”

Investigation of Numerical Dissipation in Classical and Implicit Large Eddy Simulations

“…The aforementioned contributions made attempts to obtain very accurate results within the framework of LES and ILES methods to gain a deeper insight into the behaviour of the physics of turbulence. The reader can refer to the application of the ILES method in different contexts [14][15][16][17][18], where the quantification of numerical dissipation and dispersion could also be employed to improve the accuracy of the numerical solution.…”

Micro/mesoscale combustion based portable power generating system

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