Theory and application of 3‐D LSKUM based on entropy variables

Deshpande, S. M.; Anandhanarayanan, K.; Praveen, C.; Ramesh, V.

doi:10.1002/fld.266

Cited by 30 publications

(17 citation statements)

References 7 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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“…These variables have been used by Dauhoo, Ghosh, Ramesh and Deshpande 9 and by Deshpande, Anandhanarayanan, Praveen and Ramesh 13 . For 1-D problem, the q-variables are defined by g -ë û Given U or q, we can construct a unique Maxwellian denoted by F or F(q).…”

Section: Q-lskum Methodsmentioning

confidence: 99%

“…(iv) Iterations or some kind of inner iterations are required to obtain higher accurate values of xo f from Eqn. (13). One possible of cycle of iterations could be ( ) Let us get back to first-order LS formula in Eqn.…”

Section: Least Squares Discretisationmentioning

confidence: 99%

Least squares Kinetic Upwind Mesh-free Method

Deshpande¹,

Ramesh²,

Malagi³

et al. 2010

DSJ

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Least squares kinetic upwind mesh-free (LSKUM) method has been the subject of research over twenty years in our research group. LSKUM method requires a cloud (W) of points or nodes and connectivity N(P 0 ) for every 0 P Î W . The connectivity of P 0 is a set of neighboursThe cloud can be a simple cloud, Cartesian cloud or chimera cloud or can be obtained rapidly using advancing front method. The discrete approximation to spatial derivatives was obtained using of least squares and it can be made accurate using defect correction method. The LSKUM first operates on the Boltzmann level and then passes on to Euler or Navier-Stokes level by taking suitable moments (so called y moments) of the Boltzmann equation of kinetic theory of gases. The upwinding in LSKUM method is enforced by stencil or connectivity splitting based on the signs of v 1 , v 2 in 2-D and v 1 , v 2 , v 3 in 3-D. This leads to split fluxes encountered in Kinetic Flux Vector Splitting (KFVS) method. The higher-order accurate LSKUM method can be made more efficient using entropy variables, thus leading to q-LSKUM method. Lastly, boundary conditions are implemented using specular reflection model on the wall (KCBC method) and by using kinetic outer boundary condition (KOBC) method for a point on the outer boundary.

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“…Both of them have used the least square procedure to approximate spatial derivatives. Deshpande and colleagues have developed a meshless Euler solver called the Least Square Kinetic Upwind Method (LSKUM; Deshpande, Anandhanarayanan, Praveen, & Ramesh, 2002;Deshpande, Kulkarni, & Ghosh, 1998;Ghosh & Deshpande, 1995;Ramesh, 2001;Ramesh & Deshpande, 2001, 2004, 2007Ramesh, Mathur, & Deshpande, 1997). Balakrishnan (2003, 2006) have developed a meshless solver based on the finite difference approach called the Least Square Upwind Finite Difference Method (LSFD-U).…”

Section: Introductionmentioning

confidence: 99%

Implicit scheme for meshless compressible Euler solver

Singh

Ramesh

Balakrishnan

2015

Engineering Applications of Computational Fluid Mechanics

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In this paper, an implicit scheme is presented for a meshless compressible Euler solver based on the Least Square Kinetic Upwind Method (LSKUM). The Jameson and Yoon's split flux Jacobians formulation is very popular in finite volume methodology, which leads to a scalar diagonal dominant matrix for an efficient implicit procedure . However, this approach leads to a block diagonal matrix when applied to the LSKUM meshless method. The above split flux Jacobian formulation, along with a matrix-free approach, has been adopted to obtain a diagonally dominant, robust and cheap implicit time integration scheme. The efficacy of the scheme is demonstrated by computing 2D flow past a NACA 0012 airfoil under subsonic, transonic and supersonic flow conditions. The results obtained are compared with available experiments and other reliable computational fluid dynamics (CFD) results. The present implicit formulation shows good convergence acceleration over the RK4 explicit procedure. Further, the accuracy and robustness of the scheme in 3D is demonstrated by computing the flow past an ONERA M6 wing and a clipped delta wing with aileron deflection. The computed results show good agreement with wind tunnel experiments and other CFD computations.

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Theory and application of 3‐D LSKUM based on entropy variables

Cited by 30 publications

References 7 publications

A Comparison of Various Meshless Schemes Within a Unified Algorithm

A Comparison of Various Meshless Schemes Within a Unified Algorithm

Least squares Kinetic Upwind Mesh-free Method

Implicit scheme for meshless compressible Euler solver

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