Least squares Kinetic Upwind Mesh-free Method - Deshpande, Suresh M; Ramesh, V.; Malagi, Keshav; Arora, Konark (Defence Science Journal, 2010)
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