相关论文: Space-time Non-local multi-continua upscaling for …
In this paper, we develop a space-time upscaling framework that can be used for many challenging porous media applications without scale separation and high contrast. Our main focus is on nonlinear differential equations with multiscale…
In this paper, we present an upscaling method for problems in perforated domains with non-homogeneous boundary conditions on perforations. Our methodology is based on the recently developed Non-local multicontinuum method (NLMC). The main…
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…
Time-evolving perforated domains arise in many engineering and geoscientific applications, including reactive transport, particle deposition, and structural degradation in porous media. Accurately capturing the macroscopic behavior of such…
In this paper we propose simple multiscale basis functions with constraint energy minimization to solve elliptic problems with high contrast medium. Our methodology is based on the recently developed non-local multicontinuum method (NLMC).…
We present a space-time multiscale method for a parabolic model problem with an underlying coefficient that may be highly oscillatory with respect to both the spatial and the temporal variables. The method is based on the framework of the…
This work develops a dynamic homogenization approach for metamaterials. It finds an approximate macroscopic homogenized equation with constant coefficients posed in space and time; however, the resulting homogenized equation is higher order…
In this paper, we propose a rigorous and accurate non-local (in the oversampled region) upscaling framework based on some recently developed multiscale methods [10]. Our proposed method consists of identifying multi-continua parameters via…
The present paper is concerned with a space-time homogenization problem for nonlinear diffusion equations with periodically oscillating (in space and time) coefficients. Main results consist of a homogenization theorem (i.e., convergence of…
In this paper, we discuss multiscale methods for nonlinear problems. The main idea of these approaches is to use local constraints and solve problems in oversampled regions for constructing macroscopic equations. These techniques are…
A recently developed upscaling technique, the multicontinuum homogenization method, has gained significant attention for its effectiveness in modeling complex multiscale systems. This method defines multiple continua based on distinct…
The aim of this work is the numerical homogenization of a parabolic problem with several time and spatial scales using the heterogeneous multiscale method. We replace the actual cell problem with an alternate one, using Dirichlet boundary…
This paper aims at an accurate and efficient computation of effective quantities, e.g., the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods…
This paper presents a concurrent global-local numerical method for solving multiscale parabolic equations in divergence form. The proposed method employs hybrid coefficient to provide accurate macroscopic information while preserving…
In this work, we present an efficient way to decouple the multicontinuum problems. To construct decoupled schemes, we propose Implicit-Explicit time approximation in general form and study them for the fine-scale and coarse-scale space…
In this paper, we develop and analyze a rigorous multiscale upscaling method for dual continuum model, which serves as a powerful tool in subsurface formation applications. Our proposed method is capable of identifying different continua…
This paper concerns the analysis of a multiscale method for wave propagation problems in microscopically nonhomogeneous media. A direct numerical approximation of such problems is prohibitively expensive as it requires resolving the…
Simulating diffusion in heterogeneous media presents a significant computational challenge, as resolving microscopic physical scales traditionally demands excessively fine computational grids. To overcome this barrier, we extend the…
Recently, several approaches for multiscale simulations for problems with high contrast and no scale separation are introduced. Among them is the nonlocal multicontinua (NLMC) method, which introduces multiple macroscopic variables in each…
This paper considers a time-fractional diffusion-wave equation with a high-contrast heterogeneous diffusion coefficient. A numerical solution to this problem can present great computational challenges due to its multiscale nature.…