1. A computer implemented method, with processors operating in parallel, of simulation of multiphase flow of fluids in a subterranean reservoir organized into a grid of reservoir cells, the reservoir cells having multiple interacting continua in which the multiphase fluid flow takes place, comprising the steps of: partitioning the reservoir according to the presence of collocated interacting continua in the reservoir, the collocated interacting continua of the partitioned reservoir cells having flow interchange with continua of adjacent reservoir cells; assigning a global cell number of a global cell domain to the reservoir cells where the continua are present; partitioning the global cell domain into a number of parallel data subdomains according to the number of processors operating in parallel; assigning a local cell index to the cells of the parallel data subdomains to form simulation subdomains; organizing the cells for the simulation subdomains into interior cells, boundary cells and halo cells; representing the subdomain-to-subdomain connectivities of the simulation subdomains as a dual level distribution; determining inter-continua transmissibilities and intra-continua transmissibilities for the active cells of the continua; solving simultaneously in the processors assigned the parallel data subdomains a fully-coupled set of constraint equations to determine multiphase fluid flow for the active cells of the simulation subdomains; and linearizing the solution of fully coupled nonlinear set of constraint equations.