A dimensional splitting method for quasilinear hyperbolic equations with variable coefficients (Q1963911)

A numerical method is presented for the variable coefficient nonlinear hyperbolic equation \(u_{t} + \sum_{i=1}^{d} V_{i}(x,t)f_{i}(u)_{x_{i}} = 0\) in arbitrary space dimension for bounded velocities that are Lipschitz continuous in \(x\). The method is based on dimensional splitting and uses a front tracking method to solve the resulting one-dimensional nonconservative equations. The method is unconditionally stable. The efficiency of the method is compared with a high-resolution total-variation diminishing method for a nonlinear problem, and applications to reservoir simulation are presented.