Methods have been developed to predict how hydrodynamic loads acting on nearly saturated porous media are transmitted to the subsoil. In line with the effective stress principle of Terzaghi, these methods apply the boundary conditions that the effective stresses at the surface of a porous medium are zero, and that the pore water pressures carry the full load. Here, a new approach is presented which is based on defining a stress and a stress gradient as boundary conditions. The stress gradient follows from the momentum balance equation, thereby assuring that the solution abides by d'Alembert's principle of minimization of virtual work. The corresponding solution is in full accordance with the volume and momentum balance equations of the linear elastic soil matrix and the volume and momentum balance equations of the pore water across the computational domain. The new method is thereby able to correctly reproduce measurements of pore pressure changes due to hydrodynamic loads under the assumption of a porous medium consisting of incompressible particles and pore water which could either be compressible or incompressible. The advantage of the proposed method is that it requires one less boundary condition at the surface of the porous medium. The method is therefore able to predict the magnitude of the effective stresses on a soil surface. Due to the ability to retain the assumption of incompressible water, the method has also become independent on a calibration parameter. The results of the method induce questions with respect to the validity of Terzaghi's principle of effective stress at the boundary when porous media are subjected to hydrodynamic loads.

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We present our short series of interactive animations on directional derivatives and level curves. This visualisation was developed for students of first-year mathematics courses at the Delft University of Technology. The interactive animation is an animated video that can be interacted with while it is paused or playing. The user can change, for example, the function that is plotted, drag points of interest or change the angle of the camera to explore the scene.

Many physical phenomena can be described as the evolution of two phases coexisting within the same domain. Examples of such phenomena are the transport of gas and oil, solidification and phase transformations. Each of these phenomena require a description of the dynamics under which the phases change and a technique for tracking the interface between the relevant phases. Currently several techniques exist for describing the evolution of an interface between two phases. We can distinguish these techniques as either interface-tracking or interface-capturing. Interface-tracking techniques commonly describe the interface exactly, for example by representing the interface explicitly in a mesh [15], by assuming a parametric shape of the interface (See for example [19]) or by introducing markers indicating one of the phases [7] or the interface [4], and tracking explicitly the evolution of this interface. The class of interface-capturing techniques describe the interface implicitly by a function, such as the level-set method [12], the volume-of-fluid method [9] and the moment-of-fluid method [5], and track the evolution of this function explicitly. Recently, both methods have been combined to exploit the ease of capturing the location of the interface from the level-set method and the volume-preserving capacities of the volume-of-fluid method. So far, this coupling has only been performed on regular quadrilateral meshes adopting finite-volume discretisations [17] and on triangular meshes in the context of discontinuous-Galerkin finite-elements. In this article we develop a volume-preserving level-set method by coupling a Galerkin level-set formulation based on linear triangles with the volume-of-fluid method on star-shaped polygonal finite-volume meshes. This article will first introduce introduce the level-set method and the volume-of-fluid method and our choice of discretisation for each of the methods. Subsequently we will define the coupling between the two methods and the novel volume-correction algorithm which will ensure volume preservation during advection of the level-set and volume-of-fluid functions. Finally we will investigate the numerical and practical aspects of the volume-correction algorithm by several examples.