2026-09-22T13:05:41Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/21160 2023-07-10 col_2142_5131 col_2142_11615 com_2142_5130 com_2142_9130 com_2142_8903

Higdon, Jonathan J.L. Muldowney, Gregory Patrick 2011-05-07T13:00:08Z 2011-05-07T13:00:08Z 10000-01-01 1989 "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." Made available in DSpace on 2011-05-07T13:00:08Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 8916288.pdf: 7127225 bytes, checksum: e60d31c836400d88db68a0d9a6e377ed (MD5) Previous issue date: 1989 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:48:53Z Item is restricted indefinitely. Restriction data tranferred 2014-07-01T11:22:11-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission ETDs are only available to UIUC Users without author permission U of I Only AAI8916288 (UMI)AAI8916288 http://hdl.handle.net/2142/21160 eng Copyright 1989 Muldowney, Gregory Patrick Engineering, Chemical Simulation of time-dependent free surface Navier-Stokes flows text Chemical and Biomolecular Engineering Chemical Engineering University of Illinois at Urbana-Champaign Dissertation Ph.D.