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In this work we present a multilayer shallow model to approximate the Navier-Stokes equations with hydrostatic pressure and the $\mu(I)$-rheology. The main advantages of this approximation are (i) the low cost associated with the numerical…
The novel neural networks show great potential in solving partial differential equations. For single-phase flow problems in subsurface porous media with high-contrast coefficients, the key is to develop neural operators with accurate…
Optimal-order uniform-in-time $H^1$-norm error estimates are given for semi- and full discretizations of mean curvature flow of surfaces in arbitrarily high codimension. The proposed and studied numerical method is based on a parabolic…
In this work, we present a class of new efficient models for water flow in shallow unconfined aquifers, giving an alternative to the classical but less tractable 3D-Richards model. Its derivation is guided by two ambitions: any new model…
Binary-fluid flows can be modeled using the Navier-Stokes-Cahn-Hilliard equations, which represent the boundary between the fluid constituents by a diffuse interface. The diffuse-interface model allows for complex geometries and topological…
In many interfacial flow systems, variations of surface properties lead to novel and interesting behaviors. In this work a three-dimensional model of flow dynamics for multicomponent vesicles is presented. The surface composition is modeled…
Many immersed boundary methods solve for surface stresses that impose the velocity boundary conditions on an immersed body. These surface stresses may contain spurious oscillations that make them ill-suited for representing the physical…
Similar to the notion of h-adaptivity, where the discretization resolution is adaptively changed, I propose the notion of model adaptivity, where the underlying model (the governing equations) is adaptively changed in space and time.…
Simulating the flow of two fluid phases in porous media is a challenging task, especially when fractures are included in the simulation. Fractures may have highly heterogeneous properties compared to the surrounding rock matrix,…
Applied problems of oil and gas recovery are studied numerically using the mathematical models of multiphase fluid flows in porous media. The basic model includes the continuity equations and the Darcy laws for each phase, as well as the…
In this note, the existing porousMultiphaseFoam toolbox, developed initially for any two-phase flow in porous media is extended to the specific case of the Richards' equation which neglect the pressure gradient of the non-wetting phase.…
High-fidelity, high-resolution numerical simulations are crucial for studying complex multiscale phenomena in fluid dynamics, such as turbulent flows and ocean waves. However, direct numerical simulations with high-resolution solvers are…
We propose an extension of the discretization approaches for multilayer shallow water models, aimed at making them more flexible and efficient for realistic applications to coastal flows. A novel discretization approach is proposed, in…
We present efficient deep learning techniques for approximating flow and transport equations for both single phase and two-phase flow problems. The proposed methods take advantages of the sparsity structures in the underlying discrete…
We present novel coupling schemes for partitioned multi-physics simulation that combine four important aspects for strongly coupled problems: implicit coupling per time step, fast and robust acceleration of the corresponding iterative…
Finite element methods based on cut-cells are becoming increasingly popular because of their advantages over formulations based on body-fitted meshes for problems with moving interfaces. In such methods, the cells (or elements) which are…
The correct choice of interface conditions and effective parameters for coupled macroscale free-flow and porous-medium models is crucial for a complete mathematical description of the problem under consideration and for accurate numerical…
This paper is devoted to studying the global and finite convergence of the semi-smooth Newton method for solving a piecewise linear system that arises in cone-constrained quadratic programming problems and absolute value equations. We first…
An iterative Finite Element method predicated on a linearisation of the weak form around a reference configuration is derived for general, three-dimensional, free-surface flows, including systems with moving contact lines. The method is a…
We present a new solver for massively parallel simulations of fully three-dimensional multiphase flows. The solver runs on a variety of computer architectures from laptops to supercomputers and on 65536 threads or more (limited only by the…