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Simulation of time-dependent free surface Navier-Stokes flows
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http://hdl.handle.net/2142/21160
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| Title: | Simulation of time-dependent free surface Navier-Stokes flows |
| Author(s): | Muldowney, Gregory Patrick |
| Doctoral Committee Chair(s): | Higdon, Jonathan J. L. |
| Department / Program: | Chemical and Biomolecular Engineering |
| Discipline: | Chemical Engineering |
| Degree Granting Institution: | University of Illinois at Urbana-Champaign |
| Degree: | Ph.D. |
| Genre: | Dissertation |
| Subject(s): | Engineering, Chemical |
| 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. |
| Issue Date: | 1989 |
| Type: | Text |
| Language: | English |
| URI: | http://hdl.handle.net/2142/21160 |
| Rights Information: | Copyright 1989 Muldowney, Gregory Patrick |
| Date Available in IDEALS: | 2011-05-07 |
| Identifier in Online Catalog: | AAI8916288 |
| OCLC Identifier: | (UMI)AAI8916288 |
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Graduate Theses and Dissertations at Illinois
Graduate Theses and Dissertations at Illinois -
Dissertations and Theses - Chemical and Biomolecular Engineering
Dissertations and Theses - Chemical and Biomolecular Engineering
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