Simulation of time-dependent free surface Navier-Stokes flows
Muldowney, Gregory Patrick
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https://hdl.handle.net/2142/21160
Description
Title
Simulation of time-dependent free surface Navier-Stokes flows
Author(s)
Muldowney, Gregory Patrick
Issue Date
1989
Doctoral Committee Chair(s)
Higdon, Jonathan J.L.
Department of Study
Chemical and Biomolecular Engineering
Discipline
Chemical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Chemical
Language
eng
Abstract
"Two numerical methods for simulation of time-dependent free-surface Navier-Stokes flows are developed. Both techniques are based on semi-implicit time advancement of the momentum equations, integral formulation of the spatial problem at each timestep, and spectral-element discretization to solve the resulting integral equation. Central to each algorithm is a boundary-specific solution step which permits the spatial treatment in two dimensions to be performed in O(N$\sp3$) operations per timestep despite the presence of deforming geometry. The first approach is a ""domain-integral"" formulation involving integrals over the entire flow domain of kernel functions which arise in time-differencing the Navier-Stokes equations. The second is a ""particular-solution"" formulation which replaces domain integration with an iterative scheme to generate particular velocity and pressure fields on individual elements, followed by a patching step to produce a particular solution continuous over the full domain. Two of the most difficult aspects of viscous free-surface flow simulations, namely time-dependent geometry and nontrivial boundary conditions, are well accommodated by these integral equation techniques. In addition the methods offer spectral accuracy in space and admit arbitrarily high-order discretization in time. For large-scale computations and/or long-term time advancement the domain-integral algorithm must be executed on a supercomputer to deliver results in reasonable processing time. A detailed simulation of gas-liquid flow with full resolution of the free phase boundary requires approximately five CPU hours at 80 megaflops. The particular-solution formulation is faster than the domain-integral technique by a factor of eight or more, completing the same gas-liquid flow calculation in about 36 CPU minutes. Timestepping tests of the latter method are still in progress, but the algorithm shows significant potential for making high-resolution modelling of fluid flow and other transport phenomena practical in the near future."
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