Numerical methods of solution for continuous countercurrent processes in the nonsteady state part I: Model equations and development of numerical methods and algorithms

AIChE Journal ◽  
1984 ◽  
Vol 30 (5) ◽  
pp. 770-779 ◽  
Author(s):  
K. S. Tan ◽  
I. H. Spinner
Keyword(s):  
Numerical Methods ◽  
Nonsteady State ◽  
Model Equations ◽  
Continuous Countercurrent

Application of Numerical Methods to Selected Model Equations

2020 ◽  
pp. 141-319
Author(s):  
Dale A. Anderson ◽  
John C. Tannehill ◽  
Richard H. Pletcher ◽  
Munipalli Ramakanth ◽  
Vijaya Shankar
Keyword(s):  
Numerical Methods ◽  
Model Equations

scholarly journals A reasoned overview on Boussinesq-type models: the interplay between physics, mathematics and numerics

2013 ◽  
Vol 469 (2160) ◽  
pp. 20130496 ◽  
Author(s):  
Maurizio Brocchini
Keyword(s):  
Numerical Methods ◽  
Finite Elements ◽  
Finite Differences ◽  
State Of The Art ◽  
Coastal Engineering ◽  
The State ◽  
Finite Volumes ◽  
International Conference ◽  
Applied Mathematician ◽  
Model Equations

This paper, which is largely the fruit of an invited talk on the topic at the latest International Conference on Coastal Engineering, describes the state of the art of modelling by means of Boussinesq-type models (BTMs). Motivations for using BTMs as well as their fundamentals are illustrated, with special attention to the interplay between the physics to be described, the chosen model equations and the numerics in use. The perspective of the analysis is that of a physicist/engineer rather than of an applied mathematician. The chronological progress of the currently available BTMs from the pioneering models of the late 1960s is given. The main applications of BTMs are illustrated, with reference to specific models and methods. The evolution in time of the numerical methods used to solve BTMs (e.g. finite differences, finite elements, finite volumes) is described, with specific focus on finite volumes. Finally, an overview of the most important BTMs currently available is presented, as well as some indications on improvements required and fields of applications that call for attention.

Rigid-Body Guidance Synthesis of Four-Bar Linkages with Use of the Relative Displacement Differences of Monad Vectors

2013 ◽  
Vol 328 ◽  
pp. 437-443
Author(s):  
Cheng Zhi Wang
Keyword(s):  
Numerical Methods ◽  
Rigid Body ◽  
Relative Displacement ◽  
Model Equations

This paper innovatively use the relative displacement differences of monad vectors to model equations for synthesizing linkages. Two types of monads are analyzed and the dyads are also presented. Several synthesis examples are illustrated to validate the effective applications of the monads to modeling and solving rigid body guidance synthesis problems. Because the monads have better modularity than the dyads used before, could be directly applied to formulating the synthesizing equations for multi-bar linkages, and then the equations could be directly solved by some corresponding numerical methods, the method is particularly suitable to automatically model and solve the synthesizing problems with computer.

On the Computations of Gas-Solid Mixture Two-Phase Flow

2014 ◽  
Vol 6 (01) ◽  
pp. 49-74 ◽  
Author(s):  
D. Zeidan ◽  
R. Touma
Keyword(s):  
Numerical Methods ◽  
Numerical Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Test Cases ◽  
Two Phase ◽  
Solid Mixture ◽  
Flow Problems ◽  
Model Equations ◽  
Initial Boundary Value

AbstractThis paper presents high-resolution computations of a two-phase gas-solid mixture using a well-defined mathematical model. The HLL Riemann solver is applied to solve the Riemann problem for the model equations. This solution is then employed in the construction of upwind Godunov methods to solve the general initial-boundary value problem for the two-phase gas-solid mixture. Several representative test cases have been carried out and numerical solutions are provided in comparison with existing numerical results. To demonstrate the robustness, effectiveness and capability of these methods, the model results are compared with reference solutions. In addition to that, these results are compared with the results of other simulations carried out for the same set of test cases using other numerical methods available in the literature. The diverse comparisons demonstrate that both the model equations and the numerical methods are clear in mathematical and physical concepts for two-phase fluid flow problems.

Numerical Simulation of Flow Characteristics about Lateral Tooth Steam Seal

2014 ◽  
Vol 1070-1072 ◽  
pp. 1967-1971
Author(s):  
Wei Sheng ◽  
Zi Chao Li ◽  
Duo Jiao Guan ◽  
Zhuang Ma
Keyword(s):  
Numerical Simulation ◽  
Numerical Methods ◽  
Finite Volume Method ◽  
Engineering Design ◽  
Turbulence Model ◽  
Flow Characteristics ◽  
Leakage Rate ◽  
Lateral Tooth ◽  
Model Equations ◽  
Volume Method

Control equations were dissociated by the finite volume method, and the closed turbulence model equations were solved, and the different forms of flow characteristics and leakage condition in lateral tooth seal in turbine were analyzed by using numerical methods. The results show that the leakage rate of the lateral tooth steam seal with a single low tooth is less than that of the lateral tooth steam seal with double low teeth under different import pressure. And the leakage rate of the lateral tooth steam seal with a single low tooth or double low teeth and bottom teeth are slightly more than those without bottom teeth. It provides theoretical reference and technical support for the engineering design and transformation of steam seal in the turbine.

scholarly journals USING OF NUMERICAL METHODS FOR CALCULATION THE EQUATION FOR CLUSTERS CONCENTRATIONS IN GASEOUS MATERIALS

2013 ◽  
Vol 3 (4) ◽  
pp. 59-62
Author(s):  
Alexey Bublikov ◽  
Natalia Denisova ◽  
Tamara Segeda
Keyword(s):  
Numerical Methods ◽  
Analytical Solution ◽  
Numerical Solution ◽  
Cluster Model ◽  
Model Equations

This article describes cluster model of gaseous materials and prospects of using the model. Equations set for the calculation of different sizes clusters concentrations are presented. The authors produce numerical solution of the equation set. Results of the numerical solution are compared with the results that derived from analytical solution.

Numerical Methods

2019 ◽  
Author(s):  
Rajesh Kumar Gupta
Keyword(s):  
Numerical Methods
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