A mapping from Schrodinger equation to Navier–Stokes equations through the product-like fractal geometry, fractal time derivative operator and variable thermal conductivity

2021 ◽  
Author(s):  
Rami Ahmad El-Nabulsi ◽  
Waranont Anukool
Keyword(s):  
Thermal Conductivity ◽  
Fractal Geometry ◽  
Schrodinger Equation ◽  
Stokes Equations ◽  
Time Derivative ◽  
Variable Thermal Conductivity ◽  
Navier Stokes ◽  
Derivative Operator ◽  
Navier Stokes Equations ◽  
Fractal Time

TRIGGERING OF DETONATION PROCESSES IN PROPULSION CHAMBER

2021 ◽  
Vol 14 (2) ◽  
pp. 40-45
Author(s):  
D. V. VORONIN ◽  
Keyword(s):  
Thermal Conductivity ◽  
Numerical Modeling ◽  
Gas Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Chemically Reacting ◽  
Plane Disk ◽  
And Diffusion

The Navier-Stokes equations have been used for numerical modeling of chemically reacting gas flow in the propulsion chamber. The chamber represents an axially symmetrical plane disk. Fuel and oxidant were fed into the chamber separately at some angle to the inflow surface and not parallel one to another to ensure better mixing of species. The model is based on conservation laws of mass, momentum, and energy for nonsteady two-dimensional compressible gas flow in the case of axial symmetry. The processes of viscosity, thermal conductivity, turbulence, and diffusion of species have been taken into account. The possibility of detonation mode of combustion of the mixture in the chamber was numerically demonstrated. The detonation triggering depends on the values of angles between fuel and oxidizer jets. This type of the propulsion chamber is effective because of the absence of stagnation zones and good mixing of species before burning.

Study Method for Low Speed Flow Basic on Precondition

2014 ◽  
Vol 1070-1072 ◽  
pp. 1972-1977
Author(s):  
Lang Li ◽  
Guo Ping Cheng ◽  
Guo Quan Zhu ◽  
Wei Zhang
Keyword(s):  
Iterative Method ◽  
Stokes Equations ◽  
Time Derivative ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Low Speed ◽  
Speed Flow ◽  
Preconditioning Method ◽  
Derivative Term ◽  
Implicit Iterative Method

Based on Navier-stokes equations, Weiss-Smith matrix preconditioning method is implemented within pseudo time derivative term. AUSM+-up family schemes and LU-SGS implicit iterative method were used to solve low speed flows and were compared with literature data and theoretical value. Through comparing calculation with the literature data and theoretical value, The Results showed the preconditioning algorithm can be applied efficiently to the low speeds flow field ,All these works built foundations for further application of chemical flows.

scholarly journals METHOD OF PARALLELIZATION OF NUMERICAL ALGORITHMOF NAVIER-STOKES EQUATIONS COMPLETE SYSTEM

2016 ◽  
pp. 92-98
Author(s):  
R. E. Volkov ◽  
A. G. Obukhov
Keyword(s):  
Thermal Conductivity ◽  
Gas Flow ◽  
Stokes Equations ◽  
Swirling Flow ◽  
Three Dimensional ◽  
Computation Time ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Navier Stokes Equations ◽  
Comparison Of The Results

The article considers the features of numerical construction of solutions of the Navier-Stokes equations full system describing a three-dimensional flow of compressible viscous heat-conducting gas under the action of gravity and Coriolis forces. It is shown that accounting of dissipative properties of viscosity and thermal conductivity of the moving continuum, even with constant coefficients of viscosity and thermal conductivity, as well as the use of explicit difference scheme calculation imposes significant restrictions on numerical experiments aimed at studying the arising complex flows of gas or liquid. First of all, it is associated with a signifi- cant complication of the system of equations, the restrictions on the value of the calculated steps in space and time, increasing the total computation time. One of the options is proposed of algorithm parallelization of numerical solution of the complete Navier - Stokes equations system in the vertical spatial coordinate. This parallelization option can significantly increase the computing performance and reduce the overall time of counting. A comparison of the results of calculation of one of options of gas flow in the upward swirling flow obtained by serial and parallel programs is presented.

scholarly journals On continuity properties of semigroups in real interpolation spaces

2020 ◽  
Author(s):  
Peer Christian Kunstmann
Keyword(s):  
Banach Space ◽  
Schrodinger Equation ◽  
Continuous Semigroup ◽  
Stokes Equations ◽  
Nonlinear Schrodinger Equation ◽  
Real Interpolation ◽  
Navier Stokes ◽  
Interpolation Spaces ◽  
Navier Stokes Equations ◽  
Continuity Properties

AbstractStarting from a bi-continuous semigroup in a Banach space X (which might actually be strongly continuous), we investigate continuity properties of the semigroup that is induced in real interpolation spaces between X and the domain D(A) of the generator. Of particular interest is the case $$(X,D(A))_{\theta ,\infty }$$ ( X , D ( A ) ) θ , ∞ . We obtain topologies with respect to which the induced semigroup is bi-continuous, among them topologies induced by a variety of norms. We illustrate our results with applications to a nonlinear Schrödinger equation and to the Navier–Stokes equations on $$\mathbb {R}^d$$ R d .

SOLUTION OF THE SYSTEM OF NAVIER–STOKES EQUATIONS LINEARIZED WITH RESPECT TO THE VELOCITY WITH REGARD OF A POWER-LOW DEPENDENCE OF VISCOSITY, THERMAL CONDUCTIVITY AND THE GASEOUS MEDIUM DENSITY ON THE TEMPERATURE

2018 ◽  
pp. 448-455
Author(s):  
Nikolai Vladimirovich Malai ◽  
Nadezhda Nikolaevna Samoilova
Keyword(s):  
Thermal Conductivity ◽  
Power Series ◽  
Coordinate System ◽  
Power Law ◽  
Gaseous Medium ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Medium Density ◽  
Navier Stokes Equations ◽  
Generalized Power Series

We received the solution of the system of Navier–Stokes equations linearized with respect to the velocity in the spheroidal coordinate system with regard of a power-law dependence of viscosity, thermal conductivity and the gaseous medium density on the temperature by means of generalized power series.

Low-Speed Preconditioning for AUSM+-Up Scheme

2015 ◽  
Vol 723 ◽  
pp. 224-228
Author(s):  
Wei Peng ◽  
Guo Ping Chen ◽  
Lang Li
Keyword(s):  
Flow Field ◽  
Iterative Method ◽  
Stokes Equations ◽  
Time Derivative ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Low Speed ◽  
Preconditioning Method ◽  
Derivative Term ◽  
Implicit Iterative Method

Based on Navier-stokes equations, Weiss-Smith matrix preconditioning method is implemented within pseudo time derivative term. AUSM+-up family schemes and LU-SGS implicit iterative method were used to solve low speed flows and were compared with literature data and theoretical value. Through comparing calculation with the literature data and theoretical value, The results showed the preconditioning algorithm can be applied efficiently to the low speeds flow field, All these works built foundations for further application of chemical flows.

scholarly journals WEAK SOLUTIONS OF NAVIER–STOKES EQUATIONS CONSTRUCTED BY ARTIFICIAL COMPRESSIBILITY METHOD ARE SUITABLE

2011 ◽  
Vol 08 (01) ◽  
pp. 101-113 ◽  
Author(s):  
DONATELLA DONATELLI ◽  
STEFANO SPIRITO
Keyword(s):  
Fourier Transform ◽  
Weak Solutions ◽  
Stokes Equations ◽  
Time Derivative ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Artificial Compressibility ◽  
Artificial Compressibility Method

We prove that weak solutions constructed by artificial compressibility method are suitable in the sense of Scheffer. Using Hilbertian setting and Fourier transform with respect to time, we obtain non-trivial estimates on the pressure and the time derivative which allow us to pass to the limit.

scholarly journals Stochastic Approaches to Deterministic Fluid Dynamics: A Selective Review

Water ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 864 ◽  
Author(s):  
Ana Bela Cruzeiro
Keyword(s):  
Fluid Dynamics ◽  
Variational Principle ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Time Derivative ◽  
Probabilistic Methods ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations

We present a stochastic Lagrangian view of fluid dynamics. The velocity solving the deterministic Navier–Stokes equation is regarded as a mean time derivative taken over stochastic Lagrangian paths and the equations of motion are critical points of an associated stochastic action functional involving the kinetic energy computed over random paths. Thus the deterministic Navier–Stokes equation is obtained via a variational principle. The pressure can be regarded as a Lagrange multiplier. The approach is based on Itô’s stochastic calculus. Different related probabilistic methods to study the Navier–Stokes equation are discussed. We also consider Navier–Stokes equations perturbed by random terms, which we derive by means of a variational principle.

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