Abstract
LEZOOMPC (Lagrangian-Eulerian method with adaptively local ZOOMing and Peak/valley Capturing approach) can effectively and accurately solve linear transport equations. It has been incorporated with the Picard method to solve 1-D nonlinear transport equations in this study. It is shown from the numerical results that the nonlinear version of LEZOOMPC (named 1NLEZMPC) is capable of solve linear transport equations and nonlinear problems including Burger's equations and retarded chemical transport equations. However, the current version of 1NLEZMPC cannot adequately deal with the sharp front problem when only advection is taken into account in solving the Burger's equation.