On a weak solution for a transonic flow problem

1985 ◽  
Vol 38 (6) ◽  
pp. 797-817 ◽  
Author(s):  
Cathleen S. Morawetz
Keyword(s):  
Weak Solution ◽  
Transonic Flow ◽  
Flow Problem

scholarly journals Semi-Inverse Method of Computation in Inviscid Transonic Flows: Application to the Design of Turbomachines Blades Profiles

1981 ◽  
Author(s):  
H. Miton
Keyword(s):  
Transonic Flow ◽  
Inverse Method ◽  
Flow Problem ◽  
Order Approximation ◽  
Suction Side ◽  
Computational Technique ◽  
Input Flow ◽  
Flow Conditions ◽  
Transonic Flows ◽  
Channel Type

The present method is based on an original computational technique of quasi two-dimensional inviscid transonic flows but which takes into account the changes of entropy due to shocks. The present approach consists in a numerical 2nd order approximation of the real transonic flow problem (hyperbolic or elliptic) by an initial values problem of hyperbolic and parabolic nature respectively. Such a method applied to the flow field between two adjacent blades profiles allows starting from a prescribed distribution of velocity along blade pressure or suction side to determine the flow details inside this domain and the profile of the opposite blade wall corresponding to input flow conditions which however should be made to satisfy the periodicity conditions as at this stage the approach is of the channel type. Examples of computation for simple cases are shown which proves the validity of the method.

Toward Applying Algebraic Multigrid to Transonic Flow Problem

2010 ◽  
Vol 32 (4) ◽  
pp. 2007-2028 ◽  
Author(s):  
Shlomy Shitrit ◽  
David Sidilkover
Keyword(s):  
Transonic Flow ◽  
Flow Problem ◽  
Algebraic Multigrid

Numerical Solution of Inviscid Two-Dimensional Transonic Flow Through a Cascade

1987 ◽  
Vol 109 (1) ◽  
pp. 108-113
Author(s):  
J. Forˇt ◽  
K. Kozel
Keyword(s):  
Experimental Data ◽  
Weak Solution ◽  
Numerical Solution ◽  
Transonic Flow ◽  
Numerical Procedure ◽  
Numerical Results ◽  
Two Dimensional ◽  
System Of Difference Equations ◽  
Flow Through ◽  
Turbine Cascades

The paper presents a method of numerical solution of transonic potential flow through plane cascades with subsonic inlet flow. The problem is formulated as a weak solution with combined Dirichlet’s and Neumann’s boundary conditions. The numerical procedure uses Jameson’s rotated difference scheme and the SLOR technique to solve a system of difference equations. Numerical results of transonic flow are compared with experimental data and with other numerical results for both compressor and turbine cascades near choke conditions.

scholarly journals On a degenerate hyperbolic problem for the 3-D steady full Euler equations with axial-symmetry

2020 ◽  
Vol 10 (1) ◽  
pp. 584-615
Author(s):  
Yanbo Hu ◽  
Fengyan Li
Keyword(s):  
Fluid Dynamics ◽  
Euler Equations ◽  
Transonic Flow ◽  
Boundary Data ◽  
Flow Problem ◽  
Structure Of Solutions ◽  
Independent Variables ◽  
Regularity Structures ◽  
Hyperbolic Curve ◽  
New System

Abstract The transonic channel flow problem is one of the most important problems in mathematical fluid dynamics. The structure of solutions near the sonic curve is a key part of the whole transonic flow problem. This paper constructs a local classical hyperbolic solution for the 3-D axisymmetric steady compressible full Euler equations with boundary data given on the degenerate hyperbolic curve. By introducing a novel set of dependent and independent variables, we use the idea of characteristic decomposition to transform the axisymmetric Euler equations as a new system which has explicitly singularity-regularity structures. We first establish a local classical solution for the new system in a weighted metric space and then convert the solution in terms of the original variables.

On a Nonlinear System of Reaction-Diffusion Equations

2006 ◽  
Vol 11 (2) ◽  
pp. 115-121 ◽  
Author(s):  
G. A. Afrouzi ◽  
S. H. Rasouli
Keyword(s):  
Weak Solution ◽  
Dirichlet Boundary ◽  
Smooth Boundary ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Dirichlet Boundary Conditions ◽  
Nonlinear Elliptic System ◽  
Positive Parameter ◽  
Nonlinear Elliptic ◽  
Positive Weak Solution

The aim of this article is to study the existence of positive weak solution for a quasilinear reaction-diffusion system with Dirichlet boundary conditions,− div(|∇u1|p1−2∇u1) = λu1α11u2α12... unα1n,   x ∈ Ω,− div(|∇u2|p2−2∇u2) = λu1α21u2α22... unα2n,   x ∈ Ω, ... , − div(|∇un|pn−2∇un) = λu1αn1u2αn2... unαnn,   x ∈ Ω,ui = 0,   x ∈ ∂Ω,   i = 1, 2, ..., n,  where λ is a positive parameter, Ω is a bounded domain in RN (N > 1) with smooth boundary ∂Ω. In addition, we assume that 1 < pi < N for i = 1, 2, ..., n. For λ large by applying the method of sub-super solutions the existence of a large positive weak solution is established for the above nonlinear elliptic system.

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