EPISO - An implicit non-iterative solution procedure for the calculation of flows in reciprocating engine chambers. This paper deals with the extensions that are required to be made to the implicit noniterative PISO solution procedure in order to calculate flows in motored reciprocating engines. Firstly the three-dimensional conservation equations governing the flow processes in asymmetric engine chambers equipped with piston bowls are given in full. These equations are then cast into finite volume forms, using orthogonal curvilinear computational grids. The operator splitting technique required to handle the velocity-pressure coupling is then given in detail, along with a similar technique for the turbulence model, in this case the turbulence kinetic energy and its dissipation rate. The EPISO (Engine PISO) algorithm is then tested on a number of flow cases in order to (i) assess its performance in comparison with earlier iterative methods, (ii) examine the temporal accuracy of the operator splitting technique, and (iii) illustrate the capability of the method to handle complex geometries and turbulent flow situations. The method is found to produce time step independent solutions at the same time step as fully implicit iterative schemes, but it is nearly an order of magnitude faster than procedures based on the SIMPLE algorithm. The algorithm is also shown to be capable of calculating three- dimensional turbulent flows in engines equipped with curvilinear piston bowls.