Convergence Acceleration of Mesh-less Euler Solver

Least Square Kinetic Upwind Method (LSKUM) is one class of mesh-less approach to solve compressible-Euler equations of gas dynamics. LSKUM is kinetic theory based upwind scheme that operates on any cloud of points. The present solver uses single step modified CIR (MCIR) scheme which is similar to first order LSKUM formulation and provides spatial accuracy closer to second order. The explicit time integration schemes like four stage Runge-Kutta (RK4) is slow in convergence. The implicit schemes offer superior robustness and faster convergence. The implicit Lower-Upper Symmetric Gauss-Seidel (LU-SGS) scheme is very attractive for its low numerical complexity, moderate memory requirement and unconditional stability for linear wave equation. It is based on the factorization of the implicit operator in to three parts namely lower triangular matrix, upper triangular matrix and diagonal terms. The use of LU-SGS results in a matrix free implicit framework which is very economical as against other expensive procedure which necessarily involves matrix inversion. In the present work LU-SGS procedure is adopted for mesh-less approach and implemented in 2-D and 3-D solvers in matrix free framework. To assess the efficacy of implicit procedure, explicit and implicit 2-D solvers are tested on NACA 0012 airfoil for various flow conditions in subsonic and transonic regime. The computed 2-D results are validated against NASA experimental data and AGRAD test case. A maximum speed of close to 14 is achieved. 3-D implicit solver is tested on ONERA M6 wing. The computed results compare very well with experiments. To demonstrate the effectiveness of code in handling small gaps, implicit solver is used to compute flow past clipped delta wing with aileron deflection of 6 at Mach number of 0.9 and angle of attack of 3. The computed results are validated with NASA experiments