A Travelling Wave Solution for Nonlinear Colloid Facilitated Mass Transport in Porous Media

2020 ◽  
pp. 103-108
Author(s):  
Salvatore Cuomo ◽  
Fabio Giampaolo ◽  
Gerardo Severino
Keyword(s):  
Porous Media ◽  
Mass Transport ◽  
Wave Solution ◽  
Travelling Wave ◽  
Travelling Wave Solution ◽  
Transport In Porous Media

scholarly journals EVOLUTION OF MODULATIONAL INSTABILITY IN TRAVELLING WAVE SOLUTION OF NON-LINEAR PARTIAL DIFFERENTIAL EQUATION

2020 ◽  
Vol 5 (1) ◽  
pp. 1-7
Author(s):  
Ram Dayal Pankaj ◽  
Arun Kumar ◽  
Chandrawati Sindhi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Wave Solution ◽  
Modulational Instability ◽  
Nonlinear Partial Differential Equation ◽  
Linear Partial Differential Equation ◽  
Travelling Wave ◽  
Travelling Wave Solution ◽  
Partial Differential ◽  
Jacobian Elliptic Functions

The Ritz variational method has been applied to the nonlinear partial differential equation to construct a model for travelling wave solution. The spatially periodic trial function was chosen in the form of combination of Jacobian Elliptic functions, with the dependence of its parameters

SHEMAT-Suite: a parallel open source simulator for flow, heat and mass transport in porous media

2021 ◽  
Author(s):  
Johannes Keller ◽  
Johanna Fink ◽  
Norbert Klitzsch
Keyword(s):  
Porous Media ◽  
Mass Transport ◽  
Open Source ◽  
Source Code ◽  
Modular Structure ◽  
Numerical Code ◽  
Heat And Mass Transport ◽  
Transport In Porous Media ◽  
Wide Range ◽  
Flow Heat

<p>We present SHEMAT-Suite, a numerical code for simulating flow, heat, and mass transport in porous media that has been published as an open source code recently. The functionality of SHEMAT-Suite comprises pure forward computation, deterministic Bayesian inversion, and stochastic Monte Carlo<br>simulation and data assimilation. Additionally, SHEMAT-Suite features a multi-level OpenMP parallelization. Along with the source code of the software, extensive documentation and a suite of test models is provided.</p><p>SHEMAT-Suite has a modular structure that makes it easy for users to adapt the code to their needs. Most importantly, there is an interface for defining the functional relationship between dynamic variables and subsurface parameters. Additionally, user-defined input and output can be implemented without interfering with the core of the code. Finally, at a deeper level, linear solvers and preconditioners can be added to the code.</p><p>We present studies that have made use of the code's HPC capabilities. SHEMAT-Suite has been applied to large-scale groundwater models for a wide range of purposes, including studying the formation of convection cells, assessing geothermal potential below an office building, or modeling submarine groundwater discharge since the last ice age. The modular structure of SHEMAT-Suite has also led to diverse applications, such as glacier modeling, simulation of borehole heat exchangers, or Optimal Experimental Design applied to the placing of geothermal boreholes.</p><p>Further, we present ongoing developments for improving the performance of SHEMAT-Suite, both by refactoring the source code and by interfacing SHEMAT-Suite with up-to-date HPC software. Examples of this include interfacing SHEMAT-Suite with the Portable Data Interface (PDI) for improved data management, interfacing SHEMAT-Suite with PetSC for MPI-parallel solvers, and interfacing SHEMAT-Suite with PDAF for parallel EnKF algorithms.</p><p>The goal for the open source SHEMAT-Suite is to provide a rigorously tested core code for flow, heat and transport simulation, Bayesian and stochastic inversion, while at the same time enabling a wide range of scientific research through straightforward user interaction.</p>

Coupled surface and grain boundary motion: a travelling wave solution

2004 ◽  
Vol 59 (8) ◽  
pp. 1267-1292 ◽  
Author(s):  
J KANEL ◽  
A NOVICKCOHEN ◽  
A VILENKIN
Keyword(s):  
Grain Boundary ◽  
Wave Solution ◽  
Travelling Wave ◽  
Travelling Wave Solution ◽  
Boundary Motion ◽  
Grain Boundary Motion

scholarly journals Travelling Waves of a Diffusive Epidemic Model with Latency and Relapse

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
Zhiping Wang ◽  
Rui Xu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Epidemic Model ◽  
Wave Solution ◽  
Local Stability ◽  
Travelling Waves ◽  
Upper And Lower Solutions ◽  
Travelling Wave ◽  
Spatial Diffusion ◽  
Travelling Wave Solution

An SEIR epidemic model with relapse and spatial diffusion is studied. By analyzing the corresponding characteristic equations, the local stability of each of the feasible steady states to this model is discussed. The existence of a travelling wave solution is established by using the technique of upper and lower solutions and Schauder's fixed point theorem. Numerical simulations are carried out to illustrate the main results.

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