New developments in kinetic schemes

Deshpande, S. M.; Kulkarni, P. S.; Ghosh, Arnab

doi:10.1016/s0898-1221(97)00259-9

Cited by 26 publications

(14 citation statements)

References 18 publications

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“…The FPM method used a polynomial basis, echoing themes from the classical finite element method. Least squares methods based on Taylor series expansions have been used extensively by Deshpande and others [7][8][9][10][11][12][13][14][15] in the context of kinetic schemes for the Euler equations. They have developed extensive capabilities with the least squares kinetic upwind method (LSKUM).…”

Section: Introductionmentioning

confidence: 99%

A Comparison of Various Meshless Schemes Within a Unified Algorithm

Jameson

2009

47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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An algorithm for use with several meshless schemes is presented based on a local extremum diminishing property. The scheme is applied to the Euler equations in two dimensions. The algorithm is suitable for use with many meshless schemes, three of which are detailed here. First, a method based on Taylor series expansion and least squares is highlighted. Next, a similar least squares method is used, but using polynomial basis functions with fixed Gaussian weighting. A third method makes use of the Hardy multiquadric radial basis functions on a local cloud of points. Results indicate that all three methods perform essentially equally well for flows without shocks. For flows with shocks, the least squares methods perform significantly better than the radial basis method, which displays discrepancies in shock location and magnitude. All methods are compared to an established finite volume method for validation purposes.

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Section: Introductionmentioning

confidence: 99%

A Comparison of Various Meshless Schemes Within a Unified Algorithm

Jameson

2009

47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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“…Second order accuracy is achieved through a twostep procedure called defect correction [16,21,22]. The defect correction is applied using q-variables introduced by Deshpande [11] while studying the symmetric hyperbolic form of Euler equations.…”

Section: Q-variables and Defect Correctionmentioning

confidence: 99%

Positivity preservation, stencil selection and applications of LSKUM to 3-D inviscid flows

2009

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“…One major di culty in studying the issue of ux conservation for grid-free schemes is that the neighbourhood connectivity of a point consists of overlapping sets of quadrilaterals, triangles (in 2D), hexahedrals or tetrahedrals (in 3D), which is quite unlike the situation in the case of ÿnite volume methods. Deshpande et al [25] have made preliminary studies on the issue of ux conservation for the least-squaresbased kinetic schemes. A similar analysis is applicable for the present scheme.…”

Section: A Note On Ux Conservation For the Grid-free Relaxation Schemementioning

confidence: 99%

A grid‐free upwind relaxation scheme for inviscid compressible flows

Balasubramanyam

Rao

2005

Numerical Methods in Fluids

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SUMMARYA new grid-free upwind relaxation scheme for simulating inviscid compressible ows is presented in this paper. The non-linear conservation equations are converted to linear convection equations with nonlinear source terms by using a relaxation system and its interpretation as a discrete Boltzmann equation. A splitting method is used to separate the convection and relaxation parts. Least squares upwinding is used for discretizing the convection equations, thus developing a grid-free scheme which can operate on any arbitrary distribution of points. The scheme is grid free in the sense that it works on any arbitrary distribution of points and it does not require any topological information like elements, faces, edges, etc. This method is tested on some standard test cases. To explore the power of the grid-free scheme, solution-based adaptation of points is done and the results are presented, which demonstrate the e ciency of the new grid-free scheme.

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New developments in kinetic schemes

Cited by 26 publications

References 18 publications

A Comparison of Various Meshless Schemes Within a Unified Algorithm

A Comparison of Various Meshless Schemes Within a Unified Algorithm

Positivity preservation, stencil selection and applications of LSKUM to 3-D inviscid flows

A grid‐free upwind relaxation scheme for inviscid compressible flows

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