Least squares Kinetic Upwind Mesh-free Method

  • Suresh M Deshpande Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore
  • V. Ramesh National Aerospace Laboratory, Bangalore
  • Keshav Malagi National Aerospace Laboratory, Bangalore
  • Konark Arora Defence Research & Development Laboratory, Hyderabad
DOI: https://doi.org/10.14429/dsj.60.579
Keywords: Boltzmann equation, kinetic theory, LSKUM method, Chimera cloud, Cartesian cloud, mesh-free method, gas dynamics, Euler equation

Abstract

Least squares kinetic upwind meshfree (LSKUM) method has been the subject of research over twenty years in our research group. LSKUM method requires a cloud Ω of points or nodes and connectivity NP0 for every P0 € Ω. The connectivity of P0 is a set of neighbours Pi€ N(P0) of P0. The cloud can be simple cloud, Cartesian cloud or chimera cloud or can be obtained rapidly by using advancing front method. The discrete approximation to spatial derivatives is obtained by use of least squares and it can be made accurate by 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 ψ 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 v1, v2 in 2D and v1, v2, v3 in 3D. This leads to split fluxes encountered in Kinetic Flux Vector Splitting KFVS method. The higher order accurate LSKUM method can be made more efficient by 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.

Defence Science Journal, 2010, 60(6), pp.583-597, DOI:http://dx.doi.org/10.14429/dsj.60.579

Author Biographies

Suresh M Deshpande, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore

Prof S.M. Deshpande graduated in Electrical Engg from Nagpur University in 1963. He did his ME (Aeronautical Engineering) in 1965 and PhD in 1970 from Department of Aerospace Engineering, Indian Institute of Science, Bengaluru. Presently, he is working at the Jawaharlal Nehru Centre for Advanced Scientific Research. His research interests are computational fluid dynamics, kinetic schemes, grid-free methods, computational aero-elasticity and data assimilation.

V. Ramesh, National Aerospace Laboratory, Bangalore

Dr Ramesh graduated in Mechanical Engineering from the University Visweswaraya College of Engineering, Bengaluru University in 1988. He did his Masters and PhD in Aerospace Engineering from the Indian Institute of Science (IISc), Bengaluru. He is working as a Scientist in the Computational and Theoretical Fluid Dynamcis Division of National Aerospace Laboratory (NAL) since 1991. His research interests are in the field of CFD, Aerodynamics, Grid-free methods, computational aero-elasticity.

Keshav Malagi, National Aerospace Laboratory, Bangalore

Mr Keshav S. Malagi graduated in Mechanical Engineering from Karnataka University, Dharwad in 2001. He did his ME from IISc, Bengaluru. He is working as a Scientist in the Computational and Theoretical Fluid Dynamcis Division of NAL since 2008. His research interests are computational fluid dynamics, aerodynamics, mesh-less methods, kinetic schemes, adaptation and computational aero-elasticity.

Konark Arora, Defence Research & Development Laboratory, Hyderabad

Mr Konark Arora obtained his BE (Hon) in Aeronautical Engineering from Punjab Engineering College (PEC), Chandigarh in 1998. He obtained his ME in Aerospace Engineering and PhD in Aerospace Engineering (CFD) from IISc, Bengaluru in 2001 and 2007 respectively. Currently, he is working in the CFD Division, DOCD, DRDL, Hyderabad. His areas of interest are computational fluid dynamics, aerodynamics, kinetic schemes and mesh-less methods.

Published
2010-09-07
How to Cite
Deshpande, S., Ramesh, V., Malagi, K., & Arora, K. (2010). Least squares Kinetic Upwind Mesh-free Method. Defence Science Journal, 60(6), 583-597. https://doi.org/10.14429/dsj.60.579
Issue
Vol 60 No 6: Computational Fluid Dynamics
Section
Research Papers
Copyright (c) 2016 Defence Science Journal

 Where otherwise noted, the Articles on this site are licensed under Creative Commons License: CC Attribution-Noncommercial-No Derivative Works 2.5 India

 

Most read articles by the same author(s)