  The efficiency of reservoir simulation is important for automated history
matching (AHM) and production optimization, etc. The fast marching marching
method (FMM) has been used for efficient reservoir simulation. FMM can be
regarded as a generalised streamline method but without the need to construct
streamlines. In FMM reservoir simulation, the Eikonal equation for the
diffusive time-of-flight (DTOF) is solved by FMM and then the governing
equations are computed on the 1D DTOF coordinate. Standard FMM solves the
Eikonal equation using a 4-stencil algorithm on 2D Cartesian grids, ignoring
the diagonal neighbouring cells. In the current study, we build a 8-stencil
algorithm considering all neighbouring cells, and use local analytical
propagation speeds. In addition, a local path-correction coefficient is
introduced to further increase the accuracy of DTOF solution. Next, a
discretisation scheme is built on the 1D DTOF coordinate for efficient
reservoir simulation. The algorithm is validated on homogeneous and
heterogeneous test cases, and its potential for efficient forward simulation in
AHM is demonstrated by two examples of dimensions 2 and 6.
