A Novel Space-Time Marching Method for Solving Linear and Nonlinear Transient Problems

In this study, a novel space-time (ST) marching method is presented to solve linear and nonlinear transient flow problems in porous media. The divides the ST domain into subdomains along time axis. solutions are approximated using polyharmonic radial polynomial basis functions (RPBFs) computational domain. order proceed axis, we use numerical solution at current timespan of two as initial conditions next stage. fictitious integration (FTIM) subsequently employed equations. novelty proposed attributed division axis such that dense ill-conditioned matrices caused by excessive number boundary interior points large distances can be avoided. results demonstrate achieves high accuracy solving problems. Compared conventional methods, meshless approach provides more accurate reduces error accumulation.