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A new method is presented for the simulation of two‐dimensional, incompressible, free surface fluid flow problems. The surface marker and micro cell (SMMC) method is capable of simulating transient free surface fluid flow problems that include multivalued free surfaces, impact of free surfaces with solid obstacles and converging fluid fronts (including wave breaking). New approaches are presented for the advection of the free surface, the calculation of the tentative velocity, final velocity and pressure fields and the use of multivalued velocities to treat converging fluid fronts. Simulation results are compared with experimental results for water sloshing in a tank to demonstrate the validity of the new method. Convergence of the new method is demonstrated by a grid refinement study. © 1997 John Wiley & Sons, Ltd.

A new method of calculating the pressure field in the simulation of two-dimensional, unsteady, incompressible, free surface fluid flow by use of a marker and cell method is presented. A critical feature of the new method is the introduction of a finer mesh of cells in addition to the regular mesh of finite volume cells. The smaller (micro) cells are used only near the free surface, while the regular (macro) cells are used throughout the computational domain. The movement of the free surface is accomplished by the use of massless surface markers, while the discrete representation of the free surface for the purpose of the application of pressure boundary conditions is accomplished by the use of micro cells. In order to exploit the advantages offered by micro cells, a new general equation governing the pressure field is derived. Micro cells also enable the identification and treatment of multiple points on the free surface in a single surface macro cell as well as of points on the free surface that are located in a macro cell that has no empty neighbors. Both of these situations are likely to occur repeatedly in a free surface fluid flow simulation, but neither situation has been explicitly taken into account in previous marker and cell methods. Numerical simulation results obtained both with and without the use of micro cells are compared with each other and with theoretical solutions to demonstrate the capabilities and validity of the new method.

SUMMARYDeficiencies associated with the simulation of impacts of fluid free surfaces with solid boundaries by use of marker-and-cell methods are identified and addressed. New procedures are introduced that affect the movement of markers in cells adjacent to a solid boundary, the flags of the cells that comprise a solid boundary and the pressure boundary condition for a cell in which impact occurs. Combined with fundamental changes in the sequence of steps in the computational cycle, these new procedures allow the intentional treatment of impact. As a result, improved estimates are obtained of the pressure associated with the cells adjacent to a boundary along which impact occurs. Consequently, more appropriate adjustments are made of the tentative internal velocities associated with such cells. In addition, a special procedure is presented for the adjustment of the tentative internal velocity between two surface cells. Finally, a new cell type termed a comer cell is defined and a procedure for its treatment is presented. Numerical examples are included to illustrate the previous deficiencies associated with the simulation o l impact as well as the effectiveness of the new methods presented in this paper. Validation of the new methods is achieved by comparison with experimental results for spillage over a containment dike.

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