Numerical Simulation of the Stiff System of Equations Within the Spintronic Model

2019 ◽  
pp. 301-308 ◽  
Author(s):  
Pavlina Kh. Atanasova ◽  
Stefani A. Panayotova ◽  
Elena V. Zemlyanaya ◽  
Yury M. Shukrinov ◽  
Ilhom R. Rahmonov
Keyword(s):  
Numerical Simulation ◽  
System Of Equations ◽  
Stiff System ◽  
Stiff System Of Equations

Computational Study of Inclusion Burst via the Proton Sponge Hypothesis

2010 ◽  
Author(s):  
Eric Freeman ◽  
Lisa Mauck Weiland ◽  
Wilson S. Meng
Keyword(s):  
Computational Study ◽  
Burst Release ◽  
System Of Equations ◽  
Biological Applications ◽  
Proton Sponge ◽  
System Of Differential Equations ◽  
Governing Equations ◽  
Stiff System ◽  
Broad Array ◽  
Insight Into

Biological proteins embedded in either a biological or an engineered membrane will actively maintain electrochemical balance across that membrane through transport of fluid and charge. While membrane studies are often planar, in nature they typically take the form of inclusions (∼spherical). Study and ultimately manipulation of the protein transporter types and density, and interior/exterior states of these inclusions lend insight into burst mechanisms appropriate to a broad array of engineering and biological applications, such as intracellular burst release of a vaccine. To explore these phenomena the governing equations of each transporter, as well as the membrane state are established. The result is a model requiring the simultaneous solution of a stiff system of differential equations. Presented is the computational solution of this system of equations for a specific burst scenario — the hypothesis that a proton sponge may be employed to expedite intracellular burst release of a DNA vaccine is explored.

scholarly journals Mass and Heat Transport Models for Analysis of the Drying Process in Porous Media: A Review and Numerical Implementation

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Hong Thai Vu ◽  
Evangelos Tsotsas
Keyword(s):  
Numerical Simulation ◽  
Porous Media ◽  
Heat Transport ◽  
Diffusion Theory ◽  
System Of Equations ◽  
Numerical Implementation ◽  
Drying Process ◽  
Transport Models ◽  
Moisture Migration ◽  
Drying Models

The modeling and numerical simulation of drying in porous media is discussed in this work by revisiting the different models of moisture migration during the drying process of porous media as well as their restrictions and applications. Among the models and theories, we consider those are ranging from simple ones like the diffusion theory to more complex ones like the receding front theory, the model of Philip and de Vries, Luikov’s theory, Krischer’s theory, and finally Whitaker’s model, in which all mass, heat transport, and phase change (evaporation) are taken into account. The review of drying models as such serves as the basis for the development of a framework for numerical simulation. In order to demonstrate this, the system of equations governing the drying process in porous media resulting from Whitaker’s model is presented and used in our numerical implementation. A numerical simulation of drying is presented and discussed to show the capability of the implementation.

scholarly journals The high hall ventilation with the simplified simulation of the fan

2018 ◽  
Vol 180 ◽  
pp. 02051
Author(s):  
Martin Kyncl ◽  
Jaroslav Pelant
Keyword(s):  
Numerical Simulation ◽  
Gravitational Field ◽  
Boundary Conditions ◽  
Finite Volume Method ◽  
Riemann Problem ◽  
Finite Volume ◽  
Unstructured Meshes ◽  
System Of Equations ◽  
Computational Results ◽  
Volume Method

Here we work with the system of equations describing the non-stationary compressible turbulent multi-component flow in the gravitational field. We focus on the numerical simulation of the fan situated inside the high hall. The RANS equations are discretized with the use of the finite volume method. The original modification of the Riemann problem and its solution is used at the boundaries. The combination of specific boundary conditions is used for the simulation of the fan. The presented computational results are computed with own-developed code (C, FORTRAN, multiprocessor, unstructured meshes in general).

Numerical Simulation of a Heat Flux Around a Ballistic Model Using a Hyperbolic Quasi-Gas Dynamic System of Equations

2021 ◽  
Vol 13 (5) ◽  
pp. 844-852
Author(s):  
B. N. Chetverushkin ◽  
V. E. Borisov ◽  
A. A. Davydov ◽  
A. E. Lutsky ◽  
Ya. V. Khankhasaeva
Keyword(s):  
Numerical Simulation ◽  
Heat Flux ◽  
Dynamic System ◽  
System Of Equations ◽  
Gas Dynamic ◽  
Ballistic Model

Developing a Hybrid Three-Dimensional Model of a Plasma Cloud Undergoing Collisionless Expansion into a Rarefied Ionised Magnetized Medium

2021 ◽  
pp. 112-132
Author(s):  
A.S. Dikalyuk
Keyword(s):  
Magnetic Field ◽  
Numerical Simulation ◽  
Numerical Scheme ◽  
Three Dimensional ◽  
System Of Equations ◽  
Plasma Cloud ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Induction Equation ◽  
Simulation Results

The paper presents the results of developing a hybrid three-dimensional model of collisionless interaction in plasma flows. This model considers ions in kinetical terms (simulated as a set of individual particles) and describes electrons in terms of continuum mechanics (simulated as a fluid). We present the system of equations behind the mathematical model and the physical conditions limiting its applicability. The system includes equations describing ion motion in electromagnetic fields, the quasineutrality equation, equations for calculating the total current density, non-radiative Maxwell's equations, and the generalised Ohm's law. We outline a numerical method for solving our hybrid model equations and describe an algorithm for solving the system of equations over time. We focus on the numerical method for solving the induction equation, which takes possible discontinuous solutions into account and preserves the divergence-free condition for the magnetic field. The paper discusses the issues of increasing the spatial approximation accuracy for the numerical scheme used to solve the induction equation. We present numerical simulation results for collisionless expansion of a plasma cloud into a rarefied ionised gas in the presence of an external magnetic field. These results were obtained using our computer code that implements the hybrid model described. The paper demonstrates some numerical properties of the digital simulation developed, specifically, how the order of accuracy for the numerical scheme approximation designed to solve the induction equation affects numerical simulation results

Numerical simulation of steady state groundwater flow field in discretely fractured rocks using the Green element method with the concept of multiple interacting normal flux

2020 ◽  
Author(s):  
Tai-Sheng Liou
Keyword(s):  
Numerical Simulation ◽  
Flow Field ◽  
Groundwater Flow ◽  
Fractured Rocks ◽  
Triangular Element ◽  
System Of Equations ◽  
Boundary Segment ◽  
Grid Block ◽  
Groundwater Flow Field ◽  
Element Method

<p>Numerical simulation is an effective tool for estimating the groundwater flow field in discretely fractured rocks (DFR). Unlike most numerical simulation methods that require the discretization of the model domain, boundary element method (BEM) is renowned of waiving the spatial discretization task but focusing on solving the integral form of the governing groundwater flow equation. However, for groundwater flow simulation in DFR, the solution obtained by BEM tends to have large error in the vicinity of fracture intersection. Therefore, a new numerical scheme, the green element method (GEM) is adopted in this study. GEM is built on the same mathematical background as BEM but turns the domain discretization back on as a necessary task. Using the second Green’s identity, GEM produces a general equation that applies to each grid block by integrating the governing equation. By making use of the singular characteristic of the Green’s function, GEM transforms the integral equation into a discretized system of equations with nodal head or nodal head gradient as unknowns. The cost of discretizing the model domain is compensated by the convenience of handling the heterogeneity of the medium. Conventional GEM manages the normal flux across a boundary segment by differentiating head values from 2 nodes in an individual grid block. This approximation overlooks the mechanism of normal flux as the exchange of fluid mass between grid blocks. To take this mechanism into consideration, a modified model of normal flux is proposed if the fracture plane is discretized into triangular elements. This model expresses the normal flux across a grid boundary segment in terms of the difference of head values in two grid blocks that are connected to this segment. For convenience, the head value at the centroid of a triangular element is used to calculate the normal flux. In other words, the unknowns of a triangular element are three nodal heads plus one centroidal head. Thus, the modified normal flux will be able to consider the interaction of all grid blocks that are connected to a target grid block. More importantly, the resulting global coefficient matrix is a square one and the system of equations is closed. The solution obtained from the closed system of equations will be exact but not a least-square approximated one. This modified GEM will be applied to simulate the steady state groundwater flow field in discretely fractured rocks.</p>

Water uptake by substituted amylose tablets: experimentation and numerical simulation

2009 ◽  
Vol 00 (00) ◽  
pp. 090904073309027-8
Author(s):  
H.W. Wang ◽  
S. Kyriacos ◽  
L. Cartilier
Keyword(s):  
Numerical Simulation ◽  
Water Uptake
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