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The mild-slope equation and its various modifications aim to model, with varying degrees of success, linear water wave propagation over sloping or undulating seabed topography. However, despite multiple modifications and attempted…
We present compatible finite element space discretizations for the ideal compressible magnetohydrodynamic equations. The magnetic field is considered both in div- and curl-conforming spaces, leading to a strongly or weakly preserved…
We present a three-dimensional model, based on cohesive spherical particles, of rain-induced landslides. The rainwater infiltration into the soil follow the either the fractional or the fractal diffusion equations. We solve analytically the…
A new method is proposed for integrating the equations of motion of an elastic filament. In the standard finite-difference and finite-element formulations the continuum equations of motion are discretized in space and time, but it is then…
Turbulence remains one of the last unresolved problems of classical physics and a major bottleneck to accurate flow prediction in climate, aerospace, and energy systems. Industrial simulations therefore rely on averaged representations of…
Despite its numerical challenges, finite element method is used to compute viscous fluid flow. A consensus on the cause of numerical problems has been reached; however, general algorithms---allowing a robust and accurate simulation for any…
This article is an invitation. It is, first, an invitation to consider as a subject worthy of attention the wide range of situations where small discrete elements, either bubbles, droplets or solid particles, are embedded in turbulent…
In the study of ocean wave impact on structures, one often uses Froude scaling since the dominant force is gravity. However the presence of trapped or entrained air in the water can significantly modify wave impacts. When air is entrained…
The proposed method aims to approximate a solution of a fluid-fluid interaction problem in case of low viscosities. The nonlinear interface condition on the joint boundary allows for this problem to be viewed as a simplified version of the…
The accurate and efficient representation of atmospheric dynamics remains a central challenge in numerical weather prediction. A particular difficulty arises from the strong anisotropy of the atmosphere, in which horizontal and vertical…
We present a mechanism to explicitly couple the finite-difference discretizations of 2D acoustic and isotropic elastic wave systems that are separated by straight interfaces. Such coupled simulations allow the application of the elastic…
Many features of granular media can be modeled by a fluid of hard spheres with inelastic collisions. Under rapid flow conditions, the macroscopic behavior of grains can be described through hydrodynamic equations accounting for dissipation…
We describe a fully discrete mixed finite element method for the linearized rotating shallow water model, possibly with damping. While Crank-Nicolson time-stepping conserves energy in the absence of drag or forcing terms and is not subject…
Simulations of fluid flow in naturally fractured rocks have implications for several subsurface applications, including energy storage and extraction, and waste storage. We are interested in flow in discrete fracture networks, which…
Many important processes affecting the Earth's climate are determined by the physical properties of seawater. Desalination of seawater is a significant source of drinking wate.Since the physical properties of seawater governing these…
Open problems in fluid dynamics, such as the existence of finite-time singularities (blowup), explanation of intermittency in developed turbulence, etc., are related to multi-scale structure and symmetries of underlying equations of motion.…
Computational fluid dynamics is a crucial tool to theoretically explore the cosmos. In the last decade, we have seen a substantial methodological diversification with a number of cross-fertilizations between originally different methods.…
The objective of this three-part work is to formulate and rigorously analyse a number of reduced mathematical models that are nevertheless capable of describing the hydrology at the scale of a river basin (i.e. catchment). Coupled surface…
Quantifying watershed process variability consistently with climate change and ecohydrological dynamics remains a central challenge in hydrology. Stochastic ecohydrology characterizes hydrologic variability through probability distributions…
Computational modeling of a complex system is limited by the parts of the system with the least information. While detailed models and high-resolution data may be available for parts of a system, abstract relationships are often necessary…