Physics-based preconditioning of Jacobian free Newton Krylov for Burgers' equation using modified nodal integral method. (November 2019) - Kumar, Niteen; Majumdar, Rudrodip; Singh, Suneet
Abstract: The application of Nodal Integral Method (NIM) is mostly limited to the low Reynolds number problems; due to lack of suitable nonlinear solvers. This necessitates the development of advanced nonlinear solvers for higher nonlinearity. Newton's method is a well-established solver for such equations. However, the rate of convergence in Newton methods is dependent on the initial guess. Additionally, the condition number of Jacobian matrix dictates the time required for matrix inversion. In this work, for the first time a preconditioner is developed for fluid flow problem using Modified-NIM (MNIM). This preconditioned Jacobian free Newton Krylov algorithm uses the linearized Modified-MNIM (M 2 NIM) as the preconditioner, resulting in better eigenvalue clustering, reducing Krylov iterations. The effectiveness of proposed method is demonstrated using 1-D Burgers' equation for larger time steps and higher Reynolds number up to 2500. The proposed preconditioner drastically reduces the spectral radius, CPU run-time and Krylov iterations. Highlights: Physics based Preconditioner is developed for Modified nodal integral method. Shock wave with high Reynolds number is simulated using large time step. Spectral analysis of preconditioned system is performed. Clustering of Eigenvalues reduces the Krylov iterations. Significant reduction in computational time is achieved.