Abstract: A method and system provide performance computing on a public grid. A computational mesh to solve a received engineering simulation (that has computations/processes) is computed. The mesh divides the CAD model up spatially into elements where conservation equations are formed. Mesh vertices identify nodes where field variables are defined. Each process owns a node/element and is assigned to a mesh partition. A solver application installed on each computer and each computer CPU spawns a thread to each CPU core. A matrix is assembled by each thread that computes numerical operators (that are stored as a coefficient matrix) that represent the conservation equations. The matrix is solved by solving the equations represented by the coefficient matrix. The solving yields field vectors that update the field variables at the nodes. The engineering solution is rendered based on the updated field variables.

Abstract: A method and system provide performance computing on a public grid. A computational mesh to solve a received engineering simulation (that has computations/processes) is computed. The mesh divides the CAD model up spatially into elements where conservation equations are formed. Mesh vertices identify nodes where field variables are defined. Each process owns a node/element and is assigned to a mesh partition. A solver application installed on each computer and each computer CPU spawns a thread to each CPU core. A matrix is assembled by each thread that computes numerical operators (that are stored as a coefficient matrix) that represent the conservation equations. The matrix is solved by solving the equations represented by the coefficient matrix. The solving yields field vectors that update the field variables at the nodes. The engineering solution is rendered based on the updated field variables.

Abstract: A numerical procedure for simulating the behavior of incompressible, viscous fluid in a casting/molding process. The method is based on classical fluid dynamic equations and uses control volume-finite element and numerical techniques to solve the momentum and energy equations to obtain solution for the variable parameters. The method incorporates five additional modules which simulate fluid flow in the shot sleeve, heat transfer between the die and the heat transfer fluid, die cooling by lubricant, formation of mend line. These additional simulation modules produce realistic boundary conditions, and replace many of the assumptions that would have to be made, to solve the governing equations. These added improvements ensure a faster convergence of the numerical solution and a more realistic simulation of the die casting process.

Abstract: The present invention provides a method for solving the Navier-Stokes equation of viscous, incompressible laminar flows with moving free surfaces in complex domains. The method uses fixed mesh control volume-finite element techniques to track the flow. A gauss point velocity vector is defined as the average of its nodal counterpart, such that the gauss point velocity vector is constant over the element. The gauss point velocity vector is then inserted into the continuity constraint to form the Poisson pressure equation for solving the pressure field. The solution to the Poisson pressure equation is unique, the common checker-board problem is therefore eliminated. The corrected pressure field is substituted into the momentum equations, so that the resulting velocity field satisfies the continuity equation. Since velocity and pressure are evaluated at the same order, the global mass conservation can be evaluated to machine round-off tolerances.