Least squares kinetic upwind method for inviscid compressible flows

Ghosh, Arnab; Deshpande, S. M.

doi:10.2514/6.1995-1735

Cited by 56 publications

(57 citation statements)

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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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“…Further, the grid-free methods are amenable for parallelisation due to uniform and simple data structure for even complex multi-bodies and hence it is easy to handle relatively moving multi-bodies in a parallel environment. Some of the notable grid-free methods that are being used in computational fluid dynamics (CFD) for compressible fluids are Deshpandes least squares kinetic upwind method (LSKUM) [1][2][3] and its extension to higher-order accuracy through entropy variables(q) called q-LSKUM 4,5 , meshless method of Batina 6 , gridless method of Morinishi 7 , finite point method (FPM) 8 , least squares finite difference-upwind (LSFD-U) method of Sridhar and Balakrishnan 9 and kinetic meshless method (KMM) of Praveen 10 . The above methods basically use least squares method for estimating spatial derivatives of fluxes.…”

Section: Introductionmentioning

confidence: 99%

Development of Three-dimensional Grid-free Solver and its Applications to Multi-body Aerospace Vehicles

Anandhanarayanan

2010

DSJ

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Grid-free solver has the ability to solve complex multi-body industrial problems with minimal effort. Grid-free Euler solver has been applied to number of multi-body aerospace vehicles using Chimera clouds of points including flight vehicle with fin deflection, nose fairing separation of hypersonic launch vehicle. A preprocessor has been developed to generate connectivity for multi-bodies using overlapped grids. Surface transpiration boundary condition has been implemented to model aerodynamic damping and to impose the relative velocity of moving components. Dynamic derivatives are estimated with reasonable accuracy and less effort using the grid-free Euler solver with the transpiration boundary condition. Further, the grid-free Euler solver has been integrated with six-degrees of freedom (6-DOF) equations of motion to form store separation dynamics suite which has been applied to obtain the trajectory of a rail launch air-to-air-missile from a complex fighter aircraft.

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“…Second-order accuracy can be obtained by using the two-step defect-correction method of Ghosh and Deshpande (1995). But, in the present work, the single-step MCIR scheme proposed by Ramesh and Deshpande (2004) has been used to obtain higher-order approximations for the spatial derivative.…”

Section: Formulationmentioning

confidence: 99%

“…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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Least squares kinetic upwind method for inviscid compressible flows

Cited by 56 publications

References 0 publications

A Comparison of Various Meshless Schemes Within a Unified Algorithm

A Comparison of Various Meshless Schemes Within a Unified Algorithm

Development of Three-dimensional Grid-free Solver and its Applications to Multi-body Aerospace Vehicles

Implicit scheme for meshless compressible Euler solver

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