Moving mesh generation for tracking a shock or steep moving front

For tracking a shack or steer moving Front in the numerical solution of Par tial Differential Algebraic Equations (PDAEs), an accurate spatial discreti zation method, Weighted Essentially Non-Oscillatory (WENO) scheme, is combi ned with moving grid techniques so that spacing of moving meshes is smoothe d locally and globally. Several monitor functions, as metric criteria of no de concentration. ale examined. While the fixed grid method (uniform grid s ize) needs many mesh points to obtain enough solution accuracy, the moving grid method (non-uniform grid size) enhances accuracy even at small mesh nu mbers but it may be prohibitive owing to the addition of complex and non-li near mesh equations into physical PDAEs. The combination of the WENO scheme (based on an adaptive stencil idea) with the moving grid techniques improv es stability and accuracy in the numerical solution over the commonly used moving grid method of central discretization. To locate adequate grid posit ion in the moving mesh method, suitable monitor function according to probl ems must be selected. (C) 2001 Elsevier Science Ltd. All rights reserved.