Current numerical simulations of laser materials processing usually simplify any process model to a great extent in order to allow for short computation times. This significantly decreases their flexibility and ability to simulate the great variation of today's processes with their subtle but important differences. The simulation presented in this paper can be said to be truly three dimensional as opposed to other reported work that uses symmetric boundary conditions. This enables the investigators to simulate real laser beams. In contrast to the (well-documented) Marangoni flow profile, the authors will show results that do not use the usual simplifying assumptions of flat surfaces. Preliminary output from the simulation deals with the transient coupled velocity and pressure profile and temperature distribution and hence the heat affected zone (HAZ). From this, conclusions can be drawn with regard to improving process efficiency, especially in laser cutting. It will be shown that the traditional perception of equating higher processing speeds with better processing efficiency does not hold in all cases. In fact, the opposite may well hold true. However, to demonstrate this the actual process of producing a part needs to be fully understood. A process may influence the workpiece material properties beneficially when it is performed at reduced speeds (material hardening or softening). The investigators contend that numerical modeling of the above can only be achieved credibly using high performance computing methods.