Mathematical Aspects of Navier Stoke's Equations
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Recent papers in Mathematical Aspects of Navier Stoke's Equations
The Navier-Stokes differential equations describe the motion of fluids which are incompressible. The three-dimensional Navier-Stokes equations misbehave very badly although they are relatively simple-looking. The solutions could wind up... more
This work is on the aerodynamics design of the body and frame of a motor tricycle using SolidWorks 2011 modeling system. Its Computational Fluid Dynamics (CFD) feature was used to run simulation tests at a target speed of 150 km/h to... more
Physics paper by Australia's Dr Peter Donald Rodgers
Physics paper by Australia's Dr Peter Donald Rodgers
This PhD thesis focuses on numerical and analytical methods for simulating the dynamics of volcanic ash plumes. The study starts from the fundamental balance laws for a multiphase gas– particle mixture, reviewing the existing models and... more
Physics paper by Australia's Dr Peter Donald Rodgers
A 3-D description of a flow past a short cyllinder shows that there is no paradox in this flow. The paradox appears only when a 2-D simplification is used.
Superrelativity is a great advancement in modern theoretical physics. Now, the relativity concepts, the quantum concepts and the navier-stokes equation concepts are in a unified field theory created by Australia's Peter Donald Rodgers.
Physics paper by Australia's Dr Peter Donald Rodgers
As continuation of method described in part 1, this paper describes how to handle with the convective terms using the method proposed in part 1
In parts 1 - 3 the method was described for solving cases of unidirectional flow. It was, obviously, an introduction to the concept of the method. In part 4 it is shown how this method can be used to solve an exemple of 2 dimensional... more
This paper describes a method for direct numerical solution of Navier Stokes Equation.
The motion of fluids which are incompressible could be described by the Navier-Stokes differential equations. However, the three-dimensional Navier-Stokes equations for modelling turbulence misbehave very badly although they are... more
The paper's focus is the calculation of unsteady incompressible 2D flows past airfoils. In the framework of the primitive variable Navier–Stokes equations, the initial and boundary conditions must be assigned so as to be compatible, to... more
This article is focused on the choice of a suitable turbulence model for simulations of an industrial pump's intake, from the perspective of accuracy and, partially, also the CPU time. Twelve steady-state and transient simulations were... more
The motion of a fluid around a circular cylinder presents interesting phenomena including flow separation, wake and turbulence. The physics of these are enshrined in the continuity equation and the Navier-Stokes Equations (NSE).... more
Applications of understanding are extracted from the Clay Mathematics Institute's paper on the Navier-Stokes equations which seeks to find a force, pressure, and initial conditions in an infinitely differentiable non-divergent vector... more
The two-dimensional simulation described in part 4 is considerably more complex than the three first parts, that threated one-dimensional flow. However, it is limited to the presence of linear therms only, which is a very limited... more
Mathematical simulation of an external 3-D flow past a short solid cylinder show some astonishing behaviour. The author invite researcher to verify the existence of such fenomena and, if found true, to review all that have been stated for... more
Stokes proposed a very ingenious method for describing 2-D flows, which uses one single equation that represents 3 different ones. However, this method is completelly useless to describe 3-D flows. Those have been a challenge to... more
As a continuation of the description of the proposed numeric method shown in parts 1 and 2, this part 3 shows how to use this method and its limits when both, convective and viscous transport of movement acts together. PART 4 IS NOW... more
In this paper, we propose a first order action functional for a large class of systems that generalize the relativistic perfect fluids in the Kaehler parametrization to noncommutative spacetimes. We calculate the equations of motion for... more
In this paper we address the problem of the quantization of the perfect relativistic fluids formulated in terms of the Kaehler parametrization. This fluid model describes a large set of interesting systems such as the power law energy... more