Simulation of time-dependent free surface Navier-Stokes flows
type: CreativeWork
description: "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 an…
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 an…
author: Muldowney, Gregory Patrick
language: eng
keywords: Engineering, Chemical
date published: 2011-05-07T13:00:08Z
date modified: 2026-07-22T22:25:17Z
provider: University of Illinois - Urbana-Champaign
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of Illinois at Urbana-Champaign

PropertyValue
property ID: Handle
value: http://hdl.handle.net/2142/21160