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A numerical model for the three-dimensional simulation of liquid-gas flows with free surfaces is presented. The incompressible Navier-Stokes equations are assumed to hold in the liquid domain. In the gas domain, the velocity is disregarded, the pressure is ...
Unlike in continuum approaches, time-dependent micro--macro calculations have been performed up to now almost exclusively using a simple explicit time marching algorithm, the exception being the pioneering work by Somasi and Khomami [J. Non-Newtonian Fluid ...
The capability of calculation of non-Newtonian flows: finite elements and stochastic simulation technique (CONNFFESSIT) to compute transient free surface flows is extended to deal with transient viscoelastic flows for domains in which the topology (connect ...
We propose a novel Eulerian algorithm to compute the changes of a glacier geometry for given mass balances. The surface of a glacier is obtained by solving a transport equation for the volume of fluid (VOF). The surface mass balance is taken into account b ...
The motion of a two-dimensional glacier is considered. At each time step, given the shape of the glacier, ice is modelled as an incompressible non-Newtonian fluid and a non-linear elliptic problem has to be solved to obtain the horizontal velocity field. T ...
A posteriori error estimates are derived for a nonlinear parabolic problem arising from the isothermal solidification of a binary alloy. Space discretization with continuous, piecewise linear finite elements is considered. The L-2 in time H-1 in space erro ...
We compute solutions of solutal phase-field models for dendritic growth of an isothermal binary alloy using anisotropic mesh refinement techniques. The adaptive strategy is based on anisotropic a posteriori estimators using a superconvergent recovery techn ...
A multiphase-field model for the description of coalescence in a binary alloy is solved numerically using adaptive finite elements with high aspect ratio. The unknown of the multiphase-field model are the three phase fields (solid phase 1, solid phase 2, a ...
A numerical model is presented for the simulation of complex fluid flows with free surfaces in three space dimensions. The model described in Maronnier et al. (J. Comput. Phys. 1999; 155(2):439) is extended to three dimensional situations. The mathematical ...
An adaptive algorithm is proposed for solving the Stokes problem with continuous, piecewise linear stabilized finite elements and meshes with high aspect ratio. Anisotropic, a posteriori error estimates in the H-1 x L-2 norm are derived, the constant being ...