Exact solutions of two dimensional flows of second order incompressible fluids

1965 ◽  
Vol 15 (1) ◽  
pp. 41-50
Author(s):  
N. Ch. Pattabhi Ramacharyulu
Keyword(s):  
Exact Solutions ◽  
Incompressible Fluids ◽  
Second Order ◽  
Two Dimensional ◽  
Two Dimensional Flows

Exact solutions for steady two-dimensional flow of a stratified fluid

1960 ◽  
Vol 9 (2) ◽  
pp. 161-174 ◽  
Author(s):  
Chia-Shun Yih
Keyword(s):  
Exact Solutions ◽  
Stratified Fluid ◽  
Two Dimensional ◽  
Wave Problem ◽  
Dimensional Flow ◽  
Lee Wave ◽  
Two Dimensional Flow ◽  
Arbitrary Amplitude ◽  
Singularity Distribution ◽  
Two Dimensional Flows

Three classes of exact solutions for steady two-dimensional flows of a stratified fluid are found. The flows which correspond to these solutions have arbitrary amplitude (however defined). Two of the three classes of solutions have close bearings on the lee-wave problem in meteorology. It is also shown that the amplitudes of the lee-wave components (if there is more than one component) depend not on the details of the shape of the barrier, but only on certain simple integral properties of the function for the singularity distribution generating the barrier.

Schemes and Applications of First and Second-Order Discrete Ordinates Interpolation Methods to Irregular Two-Dimensional Geometries

1997 ◽  
Vol 119 (4) ◽  
pp. 730-737 ◽  
Author(s):  
H.-M. Koo ◽  
K.-B. Cheong ◽  
T.-H. Song
Keyword(s):  
Exact Solutions ◽  
Second Order ◽  
Heat Fluxes ◽  
Discrete Ordinates ◽  
Analysis Tool ◽  
Two Dimensional ◽  
Numerical Schemes ◽  
Emissive Power ◽  
Square Enclosure ◽  
Good Agreement

This paper presents numerical schemes and comparison of predictions of radiative heat transfer for the first and the second order discrete ordinates methods (DOM1 and DOM2) using an interpolation scheme. The formulations are followed by derivation of numerical schemes for two-dimensional body fitted grids. With varying the optical depths and the numbers of grids and ordinates, radiative wall heat fluxes by DOM1 and DOM2 are calculated to compare with the exact solutions for three kinds of two-dimensional enclosures (square, quadrilateral, and J-shaped) containing absorbing/emitting and nonscattering media of known temperature with cold black walls. Emissive power and radiative wall heat fluxes by DOM1 and DOM2 are calculated to compare with zonal results for two-dimensional square enclosure containing absorbing/emitting and isotropically scattering medium of known uniform heat source with cold black walls. The results of DOM1 and DOM2 are in good agreement with the exact solutions or the zonal results. DOM1 gives more accurate results than DOM2 for most of the tested optical depths and the numbers of grids and ordinates. These methods appear as powerful candidates of very versatile radiation analysis tool. Their grid and ordinate dependencies are also discussed in depth.

scholarly journals Specific features of mathematical modeling of flows with detonation waves on unstructured computational grids

2017 ◽  
pp. 348-358
Author(s):  
А.И. Лопато ◽  
П.С. Уткин
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Numerical Algorithm ◽  
Plane Channel ◽  
Second Order ◽  
Computational Grids ◽  
Detonation Waves ◽  
Two Dimensional ◽  
Cellular Detonation ◽  
Two Dimensional Flows

Представлены математическая модель и вычислительный алгоритм для математического моделирования двумерных течений с волнами детонации на полностью неструктурированных расчетных сетках с треугольными ячейками. Рассмотрена задача о формировании ячеистой детонации в плоском канале для случая устойчивой детонации при различном сеточном разрешении и с использованием схем первого и второго порядков аппроксимации. A mathematical model and a numerical algorithm for the mathematical modeling of two-dimensional flows with detonation waves on fully unstructured computational grids with triangular cells are proposed. The problem concerning the formation of cellular detonation in a plane channel in the case of stable detonation for different grid resolutions and with the use of first and second order schemes is considered.

Compressible Flows Obtainable From Two-Dimensional Flows Through the Addition of a Constant Normal Velocity

1946 ◽  
Vol 13 (1) ◽  
pp. A61-A65
Author(s):  
H. Poritsky
Keyword(s):  
Steady State ◽  
Exact Solutions ◽  
Compressible Flows ◽  
Compressible Fluids ◽  
Normal Velocity ◽  
Two Dimensional ◽  
Gas Engine ◽  
Constant Magnitude ◽  
Oblique Shocks ◽  
Two Dimensional Flows

Abstract This paper demonstrates that exact solutions of the flow of compressible fluids can be obtained by starting with two-dimensional steady-state flows and superposing upon them a velocity of constant magnitude and direction at right angles to the planes of the two-dimensional flows, while at the same time, the pressure, density, and temperature of the fluid at each point are unchanged. The procedure is demonstrated by several examples, one of which is of interest in connection with the discharge of exhaust gases from a gas engine through the tail cone and tail pipe in cases where the circulation has not been completely removed from the flow. Another example is the flow around a “sweepback” or “arrow” wing. This example is illustrated for supersonic flows on plane oblique shocks and on the Meyer-Prandtl expansion around an edge.

Integrable two-dimensional dynamical systems and the characteristic Lie algebras

2007 ◽  
Vol 5 ◽  
pp. 195-200
Author(s):  
A.V. Zhiber ◽  
O.S. Kostrigina
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Second Order ◽  
System Of Equations ◽  
Two Dimensional ◽  
Finite Dimensional ◽  
Dimensional Dynamical System

In the paper it is shown that the two-dimensional dynamical system of equations is Darboux integrable if and only if its characteristic Lie algebra is finite-dimensional. The class of systems having a full set of fist and second order integrals is described.

Sign in / Sign up

Export Citation Format

Share Document