Finite-element method for time-dependent incompressible free surface flow

Boundary integral equation solution of viscous flows with free surfaces

“…The most recent developments in the field of viscous free surface flows appear to have been achieved using variations and modifications of the FE method, see for example [6][7][8][9]. The work of Silliman [6] pioneered problems in slot coating flow and this was extended by Saito and Scriven [8] to accommodate film flows with highly bent menisci by combining polar and Cartesian parametrisations of the meniscus shape.…”

An algorithm for the simulation of transient viscoelastic flows with free surfaces

“…We invoke the Galerkin principle to discretize (11)(12)(13) in space. This requires that residuals obtained after substitution of (18) in (11-13) be orthogonal to the set of basis functions, giving…”

“…Following the procedure described by Middleman [31], we have solved the dynamic problem obtained from linearization of both the governing equations (11)(12)(13)(14) and the boundary condition ( The expressions (A3) written for time t=O provide the initial conditions used in the present paper. We note that only the initial velocity field is needed for a Newtonian fluid.…”

“…Numerical methods using deforming finite element grids have been developed in the last few years for solving a broad range of moving boundary problems (Lynch [28]). In the context of Newtonian fluid mechanics, for example, Frederiksen and Watts [13] have applied the space-time -finite element method of Bonnerot and Jamet [3], while Kheshgi and Scriven [25] have suggested a Galerkin technique combined with a penalty treatment of the incompressibility constraint. A conceptual framework common to these different techniques has been established by Lynch [28]; it is adopted in the present paper, and its main features can be described as…”

Simplex space–time meshes in finite element simulations

“…BEHR and Frederiksen and Watts [4]; Jamet [5] recognized discontinuous-in-time interpolation as an advantageous approach for a model parabolic problem. This concept was then developed further for multi-dimensional advective-diffusive systems [6,7], elastodynamics [8], Navier-Stokes equations [9,10], and Navier-Stokes problems involving deforming domains [11][12][13].…”