Browsing by Author "Elsworth, D. T."

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    A numerical investigation of the artificial compressibility method for the solution of the Navier-Stokes equations
    (1992) Elsworth, D. T.; Toro, E. F.
    The Artificial Compressibility approach is an important numerical method for solving the incompressible Navier-Stokes Equations. The application of high resolution numerical methods to the equations of the artificial compressibility approach is a relatively new phenomenon and deserves further investigation. In this paper we examine the performance of five Riemann solvers: an exact Riemann solver, and four approximate solvers. The application of reflective boundary conditions is investigated, as well as the way in which the artificial compressibility coefficient is chosen.
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    Riemann solvers for solving the incompressible Navier-Stokes equations using the artificial compressibility method
    (1992) Elsworth, D. T.; Toro, E. F.
    The solution to the Incompressible Navier-Stokes equations still represents a significant numerical challenge. The reason for this is that there is a lack of coupling between velocity and pressure. This means that the equations themselves provide no way of explicitly updating the pressure field as the velocity field is advanced. The artificial compressibility approach, devised by A. J. Chorin (see Chorin 1967), represents one way of overcoming this difficulty. It is arrived at by altering the incompressible equations in such a way as to result in a system of equations in which the left hand side is hyperbolic. We wish to take advantage of the hyperbolic nature of these equations and use Riemann-problem- based-numerical-methods (or RP methods).