Related papers: Multiple solutions of nonlinear coupled constituti…
Our goal of this paper is to develop a new upscaling method for multicontinua flow problems in fractured porous media. We consider a system of equations that describes flow phenomena with multiple flow variables defined on both matrix and…
A new linear relaxation system for nonconservative hyperbolic systems is introduced, in which a nonlocal source term accounts for the nonconservative product of the original system. Using an asymptotic analysis the relaxation limit and its…
We present a framework for the simulation of rigid and deformable bodies in the presence of contact and friction. Our method is based on a non-smooth Newton iteration that solves the underlying nonlinear complementarity problems (NCPs)…
We propose a numerical scheme for simulation of transient flows of incompressible non-Newtonian fluids characterised by a non-monotone relation between the symmetric part of the velocity gradient (shear rate) and the Cauchy stress tensor…
Fluid-solid reactions exist in many chemical and metallurgical process industries. Several models describe these reactions such as volume reaction model, grain model, random pore model and nucleation model. These models give two nonlinear…
The accuracy and stability of implicit CFD codes are frequently impaired by the decoupling between variables, which can ultimately lead to numerical divergence. Coupled solvers, which solve all the governing equations simultaneously, have…
Compositional simulation is challenging, because of highly nonlinear couplings between multi-component flow in porous media with thermodynamic phase behavior. The coupled nonlinear system is commonly solved by the fully-implicit scheme.…
Nonlinearity continuation method, applied to boundary value problems for steady-state Richards equation, gradually approaches the solution through a series of intermediate problems. Originally, the Newton method with simple line search…
In this paper, we introduce a dynamical urban planning model. This leads us to study a system of nonlinear equations coupled through multi-marginal optimal transport problems. A simple case consists in solving two equations coupled through…
The central problem of strip theory is the calculation of potential flowaround 2D sections. One particular method of solutions to this problem is conformal mapping of the body section to the unit circle over which a solution of potential…
The use of mathematical models has helped to shed light on countless phenomena in chemistry and biology. Often, though, one finds that systems of interest in these fields are dauntingly complex. In this paper, we attempt to synthesize and…
In the present work, we propose a consistent and conservative model for multiphase and multicomponent incompressible flows, where there can be arbitrary numbers of phases and components. Each phase has a background fluid called the pure…
Using the theory of fixed point index, we discuss the existence and multiplicity of non-negative solutions of a wide class of boundary value problems with coupled nonlinear boundary conditions. Our approach is fairly general and covers a…
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…
In this paper, we present a multiscale method for simulations of the multicontinua unsaturated flow problems in heterogeneous fractured porous media. The mathematical model is described by the system of Richards equations for each continuum…
Fractures are normally present in the underground and are, for some physical processes, of paramount importance. Their accurate description is fundamental to obtain reliable numerical outcomes useful, e.g., for energy management. Depending…
We study several iterative methods for fully coupled flow and reactive transport in porous media. The resulting mathematical model is a coupled, nonlinear evolution system. The flow model component builds on the Richards equation, modified…
Modeling coupled processes in fractured porous media -- flow, deformation, fracture mechanics, and thermal/chemical effects -- often relies on mixed dimensional multiphysics formulations. These systems are nonlinear and depend on physical…
We establish a novel approach to probing spatially resolved multi-time correlation functions of interacting many-body systems, with scalable experimental overhead. Specifically, designing nonlinear measurement protocols for multidimensional…
This series of papers is devoted to the formulation and the approximation of coupling problems for nonlinear hyperbolic equations. The coupling across an interface in the physical space is formulated in term of an augmented system of…