Heterogeneous Mathematical Models in Fluid Dynamics and Associated Solution Algorithms

Author(s):  
Marco Discacciati ◽  
Paola Gervasio ◽  
Alfio Quarteroni
2009 ◽  
Vol 12 (3) ◽  
pp. 241-250 ◽  
Author(s):  
Petra Claeys ◽  
Ann van Griensven ◽  
Lorenzo Benedetti ◽  
Bernard De Baets ◽  
Peter A. Vanrolleghem

Mathematical models provide insight into numerous biological, physical and chemical systems. They can be used in process design, optimisation, control and decision support, as acknowledged in many different fields of scientific research. Mathematical models do not always yield reliable results and uncertainty should be taken into account. At present, it is possible to identify some factors contributing to uncertainty, and the awareness of the necessity of uncertainty assessment is rising. In the fields of Environmental Modelling and Computational Fluid Dynamics, for instance, terminology related to uncertainty exists and is generally accepted. However, the uncertainty due to the choice of the numerical solver and its settings used to compute the solution of the models did not receive much attention in the past. A motivating example on the existence and effect of numerical uncertainty is provided and clearly shows that we can no longer ignore it. This paper introduces a new terminology to support communication about uncertainty caused by numerical solvers, so that scientists become perceptive to it.


2021 ◽  
Vol 2059 (1) ◽  
pp. 012003
Author(s):  
A Burmistrov ◽  
A Raykov ◽  
S Salikeev ◽  
E Kapustin

Abstract Numerical mathematical models of non-contact oil free scroll, Roots and screw vacuum pumps are developed. Modelling was carried out with the help of software CFD ANSYS-CFX and program TwinMesh for dynamic meshing. Pumping characteristics of non-contact pumps in viscous flow with the help of SST-turbulence model were calculated for varying rotors profiles, clearances, and rotating speeds. Comparison with experimental data verified adequacy of developed CFD models.


Author(s):  
Rajnish K. Calay ◽  
Arne E. Holdo

The Computational Fluid Dynamics (CFD) is now increasingly being used for modeling industrial flows, i.e. flows which are multiphase and turbulent. Numerical modeling of flows where momentum, heat and mass transfer occurs at the interface presents various difficulties due to the wide range of mechanisms and flow scenarios present. This paper attempts to provide a summary of available mathematical models and techniques for two-phase flows. Some comments are also made on the models available in the commercially available codes.


1963 ◽  
Vol 30 (4) ◽  
pp. 481-485 ◽  
Author(s):  
L. N. Howard

This paper gives an expository survey of some of the principal mathematical models which have been used in the theory of rotating fluids, together with a discussion of several explicit examples. Some of these examples are related to geophysical fluid dynamics; others more directly to laboratory studies. In all cases the examples have been selected to illustrate some of the most important physical phenomena which are characteristic of rotating flows and distinguish them from other fluid motions. Physical concepts, such as the Taylor-Proudman effects, the Ekman boundary layer, and Rayleigh’s analogy, which have proved useful in obtaining a general understanding of rotating fluids, are presented and discussed.


2020 ◽  
Author(s):  
Silvia Bozzi ◽  
Davide Dominissini ◽  
Alberto Redaelli ◽  
Giuseppe Passoni

Abstract Pathological platelet activation induced by abnormal shear stresses is regarded as a main clinical complication in recipients of cardiovascular biomedical implantable devices and prostheses. In order to improve their performance computational fluid dynamics (CFD) has been used to evaluate flow fields and related shear stresses. More recently CFD models have been equipped with mathematical models that describe the relation between fluid dynamics variables, and in particular shear stresses, and the platelet activation state (PAS). These mathematical models typically use a Lagrangian approach to extract the shear stresses along possible platelet trajectories. However, in the case of turbulent flow, the choice of the proper turbulence closure model is still debated for both concerning its effect on Lagrangian statistics and shear stress calculation. In our study five numerical simulations of the flow through a mechanical heart valve were performed and then compared in terms of Eulerian and Lagrangian quantities: a direct numerical simulation (DNS), a large eddy simulation (LES), two Reynolds-averaged Navier-Stokes (RANS) simulations (SST k-ω and RSM) and a “Laminar” (no turbulence modelling on a Taylor microscale-based grid) simulation. Results exhibit a large variability in the PAS assessment depending on the turbulence model adopted. “Laminar” and RSM estimates of platelet activation are about 60% below DNS, while LES is 16% less. Surprisingly, PAS estimated from the SST k-ω velocity field is only 8% less than from DNS data. This appears more artificial than physical as can be inferred after comparing frequency distributions of PAS and of the different Lagrangian variables of the mechano-biological model of platelet activation. Our study indicates that turbulence closures can lead to a severe underestimation of platelet activation and suggests that turbulence should be fully resolved by DNS when assessing blood damage in blood contacting devices.


2021 ◽  
Vol 1038 ◽  
pp. 506-513
Author(s):  
Viktor Hvozd ◽  
Eugene Tishchenko ◽  
Andriy Berezovskyi ◽  
Stanislav Sidnei

The article considers and analyses the methods by which it is possible to carry out research to determine the fire resistance of elements of steel frames of industrial buildings. It is determined that it is expedient to use the means of computational fluid dynamics, which has no limitations due to the high cost, complexity, environmental friendliness and complexity in comparison with real experiments. In order to conduct the most reliable computational experiments, mathematical models of temperature and mechanical reaction to the thermal effect of fire were created, taking into account the equations of thermal conductivity, systems of differential equations of stress-strain state of solids in their numerical implementation based on the finite element method. The solution of mathematical models was carried out using computational fluid dynamics, which describes the process of heat and mass transfer in test fire furnaces during the determination of fire resistance of steel structures. According to the results of computational experiments it is shown that the limiting state of loss of bearing capacity of vertical and horizontal structures occurs due to the formation of a zone of plastic deformations taking into account the associative theory of plasticity. According to the results of computational experiments, the dependence of the limit of fire resistance on the level of applied load to structures, which is close to linear, was revealed. Based on the obtained dependences and the corresponding graphs, a technique is developed based on the use of maximum deformations of the elements with the corresponding fixation of the limit state on the loss of fire resistance in terms of bearing capacity by bending this curve.


2014 ◽  
Vol 607 ◽  
pp. 193-196
Author(s):  
Li Hong Zhu ◽  
Rui He Wang ◽  
Yong Huang ◽  
Jing Yin Wang

Plugged tee is the easilyworn part of an exhaust pipe during air drilling because of the flow of the compressed air with the entrained cutting particles. The effects of the particle size on the erosion of the plugged tee are studied by computational fluid dynamics (CFD). Mathematical models of the flow of the compressed air with the entrained cutting particles through the plugged tee are built and imported into the CFD through embedding procedures. After boundary conditions and the parameter of the particle size are given, the motion paths of cuttings in the different particle size in the plugged tee and its effects on erosion of the plugged tee are obtained. Erosions in the plugged tee are mainly distributed in the wall of the buffer segment and the joints and mainly caused by the scope of the particle size of cuttings. The motion paths and the residence time of cuttings with different particle size are different, so the erosions of the joints and the buffer segment are different.


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