Integral representations of solutions for two-dimensional viscous flow problems

1982 ◽  
Vol 5 (1) ◽  
pp. 533-547 ◽  
Author(s):  
George C. Hsiao
Keyword(s):  
Viscous Flow ◽  
Integral Representations ◽  
Two Dimensional ◽  
Flow Problems

On the Approximate Solution of Viscous-Flow Problems

1963 ◽  
Vol 30 (2) ◽  
pp. 263-268 ◽  
Author(s):  
J. A. Schetz
Keyword(s):  
Approximate Solution ◽  
Exact Solutions ◽  
Viscous Flow ◽  
Closed Form ◽  
New Method ◽  
Two Dimensional ◽  
General Technique ◽  
Closed Form Solutions ◽  
Flow Problems

The need for a general technique for the approximate solution of viscous-flow problems is discussed. Existing methods are considered and a new method is presented which results in simple closed-form solutions. The accuracy of the method is demonstrated by comparisons with the results of known exact solutions, and finally the general technique is employed to determine a new solution for the fully expanded two-dimensional laminar nozzle problem.

scholarly journals Two-Dimensional Incompressible Viscous Flow Simulation Using Velocity-Vorticity Dual Reciprocity Boundary Element Method

2004 ◽  
Vol 20 (3) ◽  
pp. 177-185 ◽  
Author(s):  
T. I. Eldho ◽  
D. L. Young
Keyword(s):  
Boundary Element Method ◽  
Viscous Flow ◽  
Boundary Element ◽  
Computational Domain ◽  
Two Dimensional ◽  
Flow Problems ◽  
Poisson Equations ◽  
Incompressible Viscous Flow ◽  
Vorticity Transport ◽  
Element Method

AbstractThis paper describes a computational model based on the dual reciprocity boundary element method (DRBEM) for the solution of two-dimensional incompressible viscous flow problems. The model is based on the Navier-Stokes equations in velocity-vorticity variables. The model includes the solution of vorticity transport equation for vorticity whose solenoidal vorticity components are obtained by solving Poisson equations involving the velocity and vorticity components. Both the Poisson equations and the vorticity transport equations are solved iteratively using DRBEM and combined to determine the velocity and vorticity vectors. In DRBEM, all source terms, advective terms and time dependent terms are converted into boundary integrals and hence the computational domain of the problem reduces by one. Internal points are considered wherever solution is required. The model has been applied to simulate two-dimensional incompressible viscous flow problems with low Reynolds (Re) number in a typical square cavity. Results are obtained and compared with other models. The DRBEM model has been found to be reasonable and satisfactory.

scholarly journals Skeleton-stabilized immersogeometric analysis for incompressible viscous flow problems

2019 ◽  
Vol 344 ◽  
pp. 421-450 ◽  
Author(s):  
Tuong Hoang ◽  
Clemens V. Verhoosel ◽  
Chao-Zhong Qin ◽  
Ferdinando Auricchio ◽  
Alessandro Reali ◽  
...  
Keyword(s):  
Viscous Flow ◽  
Flow Problems ◽  
Incompressible Viscous Flow

scholarly journals Free boundary problems in shock reflection/diffraction and related transonic flow problems

2015 ◽  
Vol 373 (2050) ◽  
pp. 20140276 ◽  
Author(s):  
Gui-Qiang Chen ◽  
Mikhail Feldman
Keyword(s):  
Free Boundary ◽  
High Speed ◽  
Free Boundary Problems ◽  
Fluid Flows ◽  
Shock Reflection ◽  
Two Dimensional ◽  
Open Problems ◽  
Boundary Problems ◽  
Flow Problems ◽  
Concave Corner

Shock waves are steep wavefronts that are fundamental in nature, especially in high-speed fluid flows. When a shock hits an obstacle, or a flying body meets a shock, shock reflection/diffraction phenomena occur. In this paper, we show how several long-standing shock reflection/diffraction problems can be formulated as free boundary problems, discuss some recent progress in developing mathematical ideas, approaches and techniques for solving these problems, and present some further open problems in this direction. In particular, these shock problems include von Neumann's problem for shock reflection–diffraction by two-dimensional wedges with concave corner, Lighthill's problem for shock diffraction by two-dimensional wedges with convex corner, and Prandtl-Meyer's problem for supersonic flow impinging onto solid wedges, which are also fundamental in the mathematical theory of multidimensional conservation laws.

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