On the Finite Increment Calculus method for stabilizing advection-diffusion equations, analysis and computation of the stabilization parameter

2011 ◽  
Vol 70 (3) ◽  
pp. 383-402
Author(s):  
Manuel Ramirez ◽  
Miguel Angel Moreles
Keyword(s):  
Diffusion Equations ◽  
Advection Diffusion ◽  
Stabilization Parameter ◽  
Finite Increment

Lie group solutions of advection-diffusion equations

2021 ◽  
Vol 33 (4) ◽  
pp. 046604
Author(s):  
Yubiao Sun ◽  
Amitesh Jayaraman ◽  
Gregory S. Chirikjian
Keyword(s):  
Lie Group ◽  
Diffusion Equations ◽  
Advection Diffusion

Analytical solutions of the space–time fractional Telegraph and advection–diffusion equations

2018 ◽  
Vol 491 ◽  
pp. 810-819 ◽  
Author(s):  
Ashraf M. Tawfik ◽  
Horst Fichtner ◽  
Reinhard Schlickeiser ◽  
A. Elhanbaly
Keyword(s):  
Analytical Solutions ◽  
Space Time ◽  
Diffusion Equations ◽  
Advection Diffusion

POSITIVITY OF k-EPSILON TURBULENCE MODELS FOR INCOMPRESSIBLE FLOW

2002 ◽  
Vol 12 (03) ◽  
pp. 393-406 ◽  
Author(s):  
ZI-NIU WU ◽  
SONG FU
Keyword(s):  
Reynolds Number ◽  
Point Source ◽  
Incompressible Flow ◽  
Iterative Procedure ◽  
High Reynolds Number ◽  
Operator Splitting ◽  
Turbulence Models ◽  
Diffusion Equations ◽  
Advection Diffusion ◽  
High Reynolds

The k-epsilon turbulence model for incompressible flow involves two advection–diffusion equations plus point-source terms. We propose a new method for positivity analysis. This method uses an iterative procedure combined with an operator splitting. With this method we recover the well-known positivity result for the standard high Reynolds number model. Most importantly, we are able to prove the positivity result for general low Reynolds number k-epsilon models.

An efficient Bi-cubic B-spline ADI method for numerical solutions of two-dimensional unsteady advection diffusion equations

2018 ◽  
Vol 28 (11) ◽  
pp. 2620-2649 ◽  
Author(s):  
Rajni Rohila ◽  
R.C. Mittal
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Solutions ◽  
Diffusion Equations ◽  
Spline Functions ◽  
Two Dimensional ◽  
Partial Differential ◽  
Content Type ◽  
B Spline ◽  
Advection Diffusion

Purpose This paper aims to develop a novel numerical method based on bi-cubic B-spline functions and alternating direction (ADI) scheme to study numerical solutions of advection diffusion equation. The method captures important properties in the advection of fluids very efficiently. C.P.U. time has been shown to be very less as compared with other numerical schemes. Problems of great practical importance have been simulated through the proposed numerical scheme to test the efficiency and applicability of method. Design/methodology/approach A bi-cubic B-spline ADI method has been proposed to capture many complex properties in the advection of fluids. Findings Bi-cubic B-spline ADI technique to investigate numerical solutions of partial differential equations has been studied. Presented numerical procedure has been applied to important two-dimensional advection diffusion equations. Computed results are efficient and reliable, have been depicted by graphs and several contour forms and confirm the accuracy of the applied technique. Stability analysis has been performed by von Neumann method and the proposed method is shown to satisfy stability criteria unconditionally. In future, the authors aim to extend this study by applying more complex partial differential equations. Though the structure of the method seems to be little complex, the method has the advantage of using small processing time. Consequently, the method may be used to find solutions at higher time levels also. Originality/value ADI technique has never been applied with bi-cubic B-spline functions for numerical solutions of partial differential equations.

scholarly journals Mathematical Models for Calculation of Mixing Zones for Coastal Effluent Discharges

2019 ◽  
Vol 8 (6S3) ◽  
pp. 97-104
Keyword(s):  
Concentration Level ◽  
Diffusion Equations ◽  
Concentration Limit ◽  
Mixing Zone ◽  
Depth Profiles ◽  
Advection Diffusion ◽  
Maximum Value ◽  
Regulatory Guidelines ◽  
The Impact

The potential long-term environmental impacts of coastal effluent discharges can be addressed and regulated using a mixing zone concept to control and manage the mixing capacity of the receiving coastal waters. The standard regulatory guidelines consist of two key elements: a concentration limit and a point of compliance expressed as a radius centered at the end of the outfall pipe. Modeling studies of the effect of seabed depth upon dispersion of coastal effluent discharges into the sea in the far-field are investigated analytically using the solutions of two-dimensional advection-diffusion equations with a point source on the simple depth profiles of a flat seabed and a uniformly sloping seabed. Solutions are then illustrated graphically by plotting contours of concentration, showing that the effluent discharged plumes are spreading downstream and heading towards the shoreline. Based on the location of maximum value of concentration at the shoreline, the imposed radius of and limit of concentration level within the circular mixing zone are formulated to be used as a measure for assessing the impact of effluent discharges in the coastal environment. The results found agreed with the mixing zones implemented in practice as the environmental quality standards by the regulatory authorities to minimize the impact. As the sea outfall's long pipeline may go beyond the continental shelf, a sudden step change in the seabed depth profiles is introduced, where the solutions of the advection-diffusion equations are obtained using the method of images. An extended formulation of the mixing zones radius and concentration limit are also presented.

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