An Implicit Finite Volume Method For
Unsteady Free Surface Flows
Author(s)
T. Chang
Abstract
Surface wave is modelled by a time-varying moving boundary. The flow problem
is solved by the finite volume formulation. This study investigates the efficacy
of flux limiters and damping coefficients on three-dimensional Euler solutions for
free surface problems. Spatial discretizations of convective fluxes based on a modified
central scheme are described. The resulting system of ordinary equations is
solved by an implicit time marching technique for the computation of waves travelling
over a submerged bar. Both kinematic and dynamic boundary conditions
are imposed at the free surface. The modified central method, stabilized by flux
limiters and a second-order damping, yields accurate solutions for computing free
surface elevations.
Keywords: unsteady, modified central method, finite volume method, free surface,
kinematic and dynamic boundary condition, implicit time stepping technique.
1 Introduction
A finite volume method using CTVD (Centered Total Variation Diminishing)
scheme has been developed to solve free surface problems of incompressible flows.
The CTVD scheme originally was devised by Sanders and Li [1] for the computation
of high-speed flows. The scheme provides high resolution shock, least
amount of numerical diffusion among TVD methods besides simple implementation
and freedom from tuning parameters. Before the application of CTVD to
the incompressible flows, one must modify the governing equations by adding a
time-derivative of the pressure term in the continuity equation so that the velocity
and pressure are coupled. This modification of continuity equation results in
a set of hyperbolic equations and the well developed time marching algorithms
for compressible flows can be readily applied in solving incompressible flows
Keywords
unsteady, modified central method, finite volume method, free surface,
kinematic and dynamic boundary condition, implicit time stepping technique.
Related Book
Other papers in this volume
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