SUMMARY This paper extends the material point method to analyze coupled dynamic, two‐phase boundary‐valued problems via a velocity formulation, in which solid and fluid phase velocities are the variables. Key components of the proposed approach are the adoption of Verruijt's sequence of update steps when integrating over time and the enhancement of volumetric strains. The connection between fractional step method and the time‐stepping algorithm presented in this paper is addressed. Enhancement of volumetric strains allows lower order variations in pressure and mitigates spurious pressure fields and locking that plague low‐order finite‐element implementations. A stress averaging technique to smoothen stress variations is proposed, and the local damping procedure adopted by FLAC is extended to handle two‐phase problems. Special Kelvin‐Voigt boundaries are developed to suppress reflections at artificial boundaries. Idealized examples are presented to demonstrate the capability of the proposed framework to accurately capture the physics of wave propagation, consolidation and wave attack on a sea dike. Copyright © 2012 John Wiley & Sons, Ltd.

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Organic compounds with surface‐active properties reduce the surface tension of water and can change soil water contact angles depending on their aqueous concentration. The presence of such compounds in the unsaturated zone affects soil moisture characteristics and unsaturated hydraulic conductivity relations, and can cause flow as a result of induced soil water pressure gradients. Some studies have used horizontal column experiments to measure the surfactant‐driven movement of water in unsaturated media; however, they have all used destructive sampling methods to determine water contents and did not measure soil water pressures. We attempted to gain better insight into this unsaturated soil water flow process through continual monitoring of water contents with time domain reflectometry and soil water pressures with pressure transducer equipped tensiometers. One half of the horizontal one‐dimensional flow cell was prewetted (but unsaturated) with water while the other half contained the same fluid content of 7% butanol solution. The temporal and spatial water content and soil water pressure information improved our understanding of the surfactant‐induced flow, including perturbations associated with solute gradients. Backflow in the flow cell was observed at later times as the water‐content‐induced component of the hydraulic gradients became more important. Hysteretic numerical simulations of the one‐dimensional horizontal flow cell using a modified version of HYDRUS 5.0 including coupled flow and transport through concentration‐dependent surface tensions were performed for the case in which butanol is the surface‐active compound. The numerical simulations, which used independently measured flow and transport parameters, provided a good fit to the experimental data and provided further insight into the induced flow behaviors.

A model is presented for simulating two‐dimensional, nonisothermal film casting of a viscous polymer. The model accommodates the effects of inertia and gravity, and allows the thickness of the film to vary across the width, but it excludes film sag and die swell. Based on the simulation results, three factors are shown to contribute to reducing neck‐in and promoting a uniform thickness: the self‐weight of the material, for low viscosity polymers; nonuniform thickness and/or velocity profiles at the die; and cooling of the film, especially when localized cooling jets are employed.

This paper presents a new numerical algorithm for 2D nonisothermal time‐stepping simulations of a nonlinear viscoelastic cast film process. A significant contribution of the algorithm is that an updated Lagrangian description of motion is employed, as opposed to the more conventional Eulerian description generally used for continuous polymer processing simulations. Furthermore, use is made of a Perzynatype constitutive equation, which is different from what is usually employed for molten polymers. The constitutive equation accommodates viscoelasticity, extensional thinning/thickening, and strain‐hardening. This new numerical algorithm can find the steady‐state film properties, and it can predict the onset of instability by observing draw resonance. The critical draw ratio is determined from the response problem, which means that the mathematical complications of the more common linear stability analysis are avoided. In terms of the stability of the film, it was observed that stability is decreased by extensional thinning, strain‐hardening, and higher relaxation times, and stability is increased by higher heat transfer coefficients and higher ratios of air‐gap length to die width.