Solving convection and convection-reaction problems using the method of lines
A spatial finite volume discretization is applied to the scalar initial-boundary value problem \(u_t+f_x(x,y,u,u_x,u_y)+g_y(x,y,u,u_x,u_y)=h(x,y,u)\), where \(f\) and \(g\) are the flux functions, \(h\) is the source term. The resulting system of ordinary differential equations is solved by using operator splitting and a new linear algebra module inside the software package SPRINT2D, especially suited for very large systems of linear equations at each time step. To obtain an accurate solution, the procedure requires an effective space-time control. The method is illustrated by solving a realistic knock-modelling combustion problem in car engines.
scientific article; zbMATH DE number 897531
scientific article