A computerized reservoir simulation of flow of multiphase fluids in wellbores of multilateral wells which have flow interchange at a plurality of locations along the extent of their lengths in the reservoir with cells of a subterranean hydrocarbon reservoir organized into a grid of reservoir cells based on input reservoir data, the reservoir cells having multiphase fluid flow taking place therein, the computer implemented method of simulating the flow of the multiphase flow of fluids comprising the steps of: partitioning the reservoir into a plurality of reservoir grid cells in a grid formed of a number of contiguous grid cells; partitioning the multilateral wellbores into a plurality of wellbore cells in a grid formed of a number of contiguous wellbore cells along the lengths of the wellbores; establishing for the reservoir grid cells representations of state changes and pressures within the reservoir grid cells and flow interchange with the wellbore cells at locations of flow interchange with the wellbore cells; establishing for the wellbore cells representations of the flow interchange with the wellbore cells and flow interchange with the reservoir grid cells at locations of flow interchange with the reservoir grid cells; forming a series preconditioner as a series based expansion by matrix-vector multiplication operations of well influence terms based on the established representations of flow interchange with the wellbore cells for the reservoir grid cells and the established representations of flow interchange with the reservoir grid cells for wellbore cells having flow interchange; applying a conjugate residual interactive matrix solution in the computer to solve the representations of flow of the multiphase fluids in the reservoir grid cells and wellbore cells to obtain a solution vector; repeating the steps of forming a series preconditioner by matrix-vector multiplication operations and applying a conjugate residual interactive matrix solution in the computer to solve for the representations of flow of the multiphase fluids of the wellbore cells until the obtained solution vector is within an established limit of accuracy; storing the computerized simulation of representations of flow of the multiphase fluids of the wellbore cells when the obtained residual is within the established limit of accuracy; and forming an output display of the stored computerized simulation of representations of flow of the multiphase fluids of the wellbore in the reservoir. partitioning the reservoir into a plurality of reservoir grid cells in a grid formed of a number of contiguous grid cells; partitioning the multilateral wellbores into a plurality of wellbore cells in a grid formed of a number of contiguous wellbore cells along the lengths of the wellbores; establishing for the reservoir grid cells representations of state changes and pressures within the reservoir grid cells and flow interchange with the wellbore cells at locations of flow interchange with the wellbore cells; establishing for the wellbore cells representations of the flow interchange with the wellbore cells and flow interchange with the reservoir grid cells at locations of flow interchange with the reservoir grid cells; forming a series preconditioner as a series based expansion by matrix-vector multiplication operations of well influence terms based on the established representations of flow interchange with the wellbore cells for the reservoir grid cells and the established representations of flow interchange with the reservoir grid cells for wellbore cells having flow interchange; applying a conjugate residual interactive matrix solution in the computer to solve the representations of flow of the multiphase fluids in the reservoir grid cells and wellbore cells to obtain a solution vector; repeating the steps of forming a series preconditioner by matrix-vector multiplication operations and applying a conjugate residual interactive matrix solution in the computer to solve for the representations of flow of the multiphase fluids of the wellbore cells until the obtained solution vector is within an established limit of accuracy; storing the computerized simulation of representations of flow of the multiphase fluids of the wellbore cells when the obtained residual is within the established limit of accuracy; and forming an output display of the stored computerized simulation of representations of flow of the multiphase fluids of the wellbore in the reservoir.