scholarly journals Elementary waves, Riemann invariants, new conservation laws and numerical method for the blood flow through artery

Authorea ◽  
2020 ◽  
Author(s):  
mahmoud abdelrahman ◽  
Kamel Mohamed
Keyword(s):  
Blood Flow ◽  
Conservation Laws ◽  
Numerical Method ◽  
Riemann Invariants ◽  
Flow Through ◽  
Elementary Waves

On the Shallow Water Equations

2017 ◽  
Vol 72 (9) ◽  
pp. 873-879 ◽  
Author(s):  
Mahmoud A.E. Abdelrahman
Keyword(s):  
Conservation Laws ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Water System ◽  
Diagonal Form ◽  
Riemann Invariants ◽  
Interesting Application ◽  
Nonlinear Conservation Laws ◽  
Shallow Water System ◽  
Elementary Waves

AbstractWe studied the shallow water equations of nonlinear conservation laws. First we studied the parametrisation of nonlinear elementary waves and hence we present the solution to the Riemann problem. We also prove the uniqueness of the Riemann solution. The Riemann invariants are formulated. Moreover we give an interesting application of the Riemann invariants. We present the shallow water system in a diagonal form, which admits the existence of a global smooth solution for these equations. The other application is to introduce new conservation laws for the shallow water equations.

A Non-Newtonian Fluid Flow Model for the Slip Condition on Blood Flow through a Stenosed Artery using Power-law Fluid

2018 ◽  
Vol 9 (7) ◽  
pp. 871-879
Author(s):  
Rajesh Shrivastava ◽  
R. S. Chandel ◽  
Ajay Kumar ◽  
Keerty Shrivastava and Sanjeet Kumar
Keyword(s):  
Blood Flow ◽  
Fluid Flow ◽  
Newtonian Fluid ◽  
Power Law ◽  
Flow Model ◽  
Slip Condition ◽  
Power Law Fluid ◽  
Stenosed Artery ◽  
Flow Through

scholarly journals Numerical Study of Blood Flow Through Artificial Heart Valves

2021 ◽  
Vol 1094 (1) ◽  
pp. 012120
Author(s):  
Hussein Togun ◽  
Ali Abdul Hussain ◽  
Saja Ahmed ◽  
Iman Abdul hussain ◽  
Huda Shaker
Keyword(s):  
Blood Flow ◽  
Artificial Heart ◽  
Heart Valves ◽  
Numerical Study ◽  
Artificial Heart Valves ◽  
Flow Through

A simple numerical method to simulate the flow through filter media: investigation of different fibre allocation algorithms

2021 ◽  
Author(s):  
Liliana Luca Xavier Augusto ◽  
Paolo Tronville ◽  
José Antônio Silveira Gonçalves ◽  
Gabriela Cantarelli Lopes
Keyword(s):  
Numerical Method ◽  
Filter Media ◽  
Flow Through ◽  
Allocation Algorithms

scholarly journals A Simple Transient Poiseuille-Based Approach to Mimic the Womersley Function and to Model Pulsatile Blood Flow

Dynamics ◽  
2021 ◽  
Vol 1 (1) ◽  
pp. 9-17
Author(s):  
Andrea Natale Impiombato ◽  
Giorgio La Civita ◽  
Francesco Orlandi ◽  
Flavia Schwarz Franceschini Zinani ◽  
Luiz Alberto Oliveira Rocha ◽  
...  
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Blood Flow ◽  
Boundary Conditions ◽  
Quadratic Function ◽  
Pulsatile Blood Flow ◽  
Flow Through ◽  
Simplified Analysis ◽  
Function Models ◽  
Flow Reversals

As it is known, the Womersley function models velocity as a function of radius and time. It has been widely used to simulate the pulsatile blood flow through circular ducts. In this context, the present study is focused on the introduction of a simple function as an approximation of the Womersley function in order to evaluate its accuracy. This approximation consists of a simple quadratic function, suitable to be implemented in most commercial and non-commercial computational fluid dynamics codes, without the aid of external mathematical libraries. The Womersley function and the new function have been implemented here as boundary conditions in OpenFOAM ESI software (v.1906). The discrepancy between the obtained results proved to be within 0.7%, which fully validates the calculation approach implemented here. This approach is valid when a simplified analysis of the system is pointed out, in which flow reversals are not contemplated.

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