A method of computerized simulation in a computer system of a plurality of data processors, including at least one central processing unit and at least one graphical processing unit , and an output display , the computerized simulation being of mixtures of, and number of phases of individual species of, component hydrocarbon fluids of a subsurface reservoir to simulate performance and production from the reservoir, the subsurface reservoir being simulated by a model partitioned into a number of cells arranged in an organized system of cells, the simulation further being based on geological and fluid characterization information for the cells of the reservoir, the method comprising the computer processing steps of: (a) receiving geological and fluid characterization information for the cells and the reservoir in the central processing unit; (b) transferring the geological and fluid characterization information to the graphical processing unit for further processing; (c) processing the transferred geological and fluid characterization information in the graphical processing unit to determine the mixture of component hydrocarbon fluids in each of the cells of the reservoir; the method characterized by : (d) processing the transferred geological and fluid characterization information in the graphical processing unit to determine the number of phases of the individual hydrocarbon species of the component fluids of each of the cells of the reservoir; (e) transferring the determined mixture of component hydrocarbon fluids and the determined number of phases of the individual hydrocarbon species of the component fluids of each of the cells of the reservoir from the graphical processing unit to the central processing unit; and (f) forming an output display of the determined mixtures of component hydrocarbon fluids and the determined number of phases of the individual hydrocarbon species of the component fluids of each of the cells of the reservoir at desired locations in the subsurface reservoir to simulate performance and production from the reservoir. (a) receiving geological and fluid characterization information for the cells and the reservoir in the central processing unit; (b) transferring the geological and fluid characterization information to the graphical processing unit for further processing; (c) processing the transferred geological and fluid characterization information in the graphical processing unit to determine the mixture of component hydrocarbon fluids in each of the cells of the reservoir; the method characterized by : (d) processing the transferred geological and fluid characterization information in the graphical processing unit to determine the number of phases of the individual hydrocarbon species of the component fluids of each of the cells of the reservoir; (e) transferring the determined mixture of component hydrocarbon fluids and the determined number of phases of the individual hydrocarbon species of the component fluids of each of the cells of the reservoir from the graphical processing unit to the central processing unit; and (f) forming an output display of the determined mixtures of component hydrocarbon fluids and the determined number of phases of the individual hydrocarbon species of the component fluids of each of the cells of the reservoir at desired locations in the subsurface reservoir to simulate performance and production from the reservoir. <EOS>