scholarly journals Homotopy Analysis Approach of Boussinesq Equation for Infiltration Phenomenon in Unsaturated Porous Medium.

2018 ◽  
Vol 7 (1) ◽  
pp. 21-28
Author(s):  
M A Patel ◽  
N B Desai
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Porous Medium ◽  
Nonlinear Partial Differential Equation ◽  
Water Reservoir ◽  
Partial Differential ◽  
Unsaturated Porous Medium ◽  
Homotopy Analysis ◽  
Convergence Control ◽  
Boussinesq’S Equation

Boussinesq’s equation is one-dimensional nonlinear partial differential equation which represents the infiltration phenomenon. This equation is frequently used to study the infiltration phenomenon in unsaturated porous medium. Infiltration is the process in which the groundwater of the water reservoir has entered in the unsaturated soil through vertical permeable wall. An approximate analytical solution of nonlinear partial differential equation is presented by homotopy analysis method. The convergence of homotopy analysis solution is discussed by choosing proper value of convergence control parameter. The solution represents the height of free surface of infiltrated water.

Unsteady Flow of Gas Through a Semi-Infinite Porous Medium

1957 ◽  
Vol 24 (3) ◽  
pp. 329-332
Author(s):  
R. E. Kidder
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Porous Medium ◽  
Gas Flow ◽  
Transient Flow ◽  
Order Term ◽  
Nonlinear Partial Differential Equation ◽  
Flow In Porous Media ◽  
Partial Differential ◽  
One Dimensional

Abstract This paper presents an analytic solution to a problem of the transient flow of gas within a one-dimensional semi-infinite porous medium. A perturbation method, carried out to include terms of the second order, is employed to obtain a solution of the nonlinear partial differential equation describing the flow of gas. The zero-order term of the solution represents the solution of the linearized partial differential equation of gas flow in porous media given by Green and Wilts (1).

scholarly journals Optimal homotopy analysis solution of fingero-imbibition phenomenon in homogeneous porous medium with magnetic fluid effect

10.29007/kq3n ◽  
2018 ◽  
Author(s):  
Dipakkumar Prajapati ◽  
Narendrasinh Desai
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Porous Medium ◽  
Magnetic Fluid ◽  
Nonlinear Partial Differential Equation ◽  
Analysis Method ◽  
Optimal Homotopy Analysis Method ◽  
Double Phase ◽  
Homotopy Analysis ◽  
Homogeneous Porous Medium

The present paper discusses the fingero-imbibition phenomenon in a double phase dis- placement process through homogeneous porous medium with the involvement of a layer of magnetic fluid in the injected phase. This phenomenon has much importance in petroleum technology. The nonlinear partial differential equation governing this phenomenon with appropriate boundary conditions is solved by an optimal homotopy analysis method. The convergence of the solution is decided by minimizing discrete squared residual.

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

Explorations and Expectations of Equidistribution Adaptations for Nonlinear Quenching Problems

2013 ◽  
Vol 5 (04) ◽  
pp. 407-422 ◽  
Author(s):  
Matthew A. Beauregard ◽  
Qin Sheng
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Finite Difference ◽  
Nonlinear Partial Differential Equation ◽  
Partial Differential ◽  
Spatial Adaptation ◽  
Monitor Function ◽  
Monitoring Strategies ◽  
Highly Nonlinear ◽  
Equidistribution Principle

AbstractFinite difference computations that involve spatial adaptation commonly employ an equidistribution principle. In these cases, a new mesh is constructed such that a given monitor function is equidistributed in some sense. Typical choices of the monitor function involve the solution or one of its many derivatives. This straightforward concept has proven to be extremely effective and practical. However, selections of core monitoring functions are often challenging and crucial to the computational success. This paper concerns six different designs of the monitoring function that targets a highly nonlinear partial differential equation that exhibits both quenching-type and degeneracy singularities. While the first four monitoring strategies are within the so-calledprimitiveregime, the rest belong to a later category of themodifiedtype, which requires the priori knowledge of certain important quenching solution characteristics. Simulated examples are given to illustrate our study and conclusions.

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