Nonlinear iteration methods for high speed laminar compressible Navier-Stokes equations

Abstract

Full Newton nonlinear iteration is compared with the use of a defect-correction approach (first-order Jacobian, second-order residual) for solving the steady-state compressible flow equations. The Jacobian is constructed numerically, and solved using a PCG-type method with block ILU(k) preconditioning. Numerical tests are carried out using the NACA 0012 airfoil, at various freestream Mach numbers and Reynolds numbers. The full Newton approximation is generally more robust and takes less CPU time than the defect-correction approach. No particular difficulty was observed in solving the full Newton Jacobian using an ILU(2) (≅ 100,000 unknowns) with CGSTAB acceleration.