A multigrid strongly implicit procedure for two-dimensional transonic potential flow problems

1982 ◽  
Author(s):  
N. SANKAR
Keyword(s):  
Potential Flow ◽  
Two Dimensional ◽  
Flow Problems ◽  
Strongly Implicit Procedure

Flows of thin streams with free boundaries

1973 ◽  
Vol 59 (3) ◽  
pp. 417-432 ◽  
Author(s):  
Joseph B. Keller ◽  
James Geer
Keyword(s):  
Channel Flow ◽  
Potential Flow ◽  
Slenderness Ratio ◽  
Asymptotic Series ◽  
Two Dimensional ◽  
Free Boundaries ◽  
Complex Flow ◽  
Flow Problems ◽  
Different Types ◽  
Wall Flow

A method is developed for determining any thin steady two-dimensional potential flow with free and/or rigid boundaries in the presence of gravity. The flow is divided into a number of parts and in each part the flow and its free boundaries are represented as asymptotic series in powers of the slenderness ratio of the stream. There are three basic flows, having two, one and no free boundaries and called jet flow, wall flow and channel flow, respectively. First the three expansions for these flows are found, extending results of Keller & Weitz (1952). They are called outer expansions to distinguish them from the inner expansions which apply near the ends of the stream or at the junction of two different types of flow. The inner and outer expansions must be matched at a junction to find how the emerging flow is related to the entering flow. This process can be continued to build up any complex flow involving thin streams. The method is illustrated in the case of a wall flow that leaves the wall to become a jet, which includes the case of a waterfall treated by Clarke (1965) in a similar way. In part 2 (to be published) other inner expansions are found and matched to outer expansions, providing the ingredients for the construction of the solutions of many flow problems.

Explicit Approximations for Calculating Potential Flow About a Body

1983 ◽  
Vol 27 (01) ◽  
pp. 1-12
Author(s):  
F. Noblesse ◽  
G. Triantafyllou
Keyword(s):  
Free Surface ◽  
Potential Flow ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Wave Resistance ◽  
Two Dimensional ◽  
Regular Waves ◽  
Practical Applications ◽  
Flow Problems ◽  
Unbounded Fluid

Several explicit approximations for calculating nonlifting potential flow about a body in an unbounded fluid are studied. These approximations are shown to be exact in the particular cases of flows due to translations of ellipsoids, and they are compared with the exact potential for two-dimensional flows about ogives in translatory motions. Two approximations, given by formulas (31) and (32) in the conclusion, appear to be of particular interest for practical applications, and they can be extended to free-surface flow problems, for example, ship wave resistance, and radiation and diffraction of regular waves by a body.

Simultaneous Solution of Multiphase Reservoir Flow Equations

1970 ◽  
Vol 10 (02) ◽  
pp. 99-110 ◽  
Author(s):  
H.G. Weinstein ◽  
H.L. Stone ◽  
T.V. Kwan
Keyword(s):  
Two Dimensions ◽  
Test Problems ◽  
Two Dimensional ◽  
Simultaneous Solution ◽  
Two Phase ◽  
Flow Problems ◽  
Reservoir Flow ◽  
Alternating Direction ◽  
Two Dimensional Flow ◽  
Strongly Implicit Procedure

Abstract A strongly implicit iterative procedure has been developed to solve systems of equations arising in multiphase, two-dimensional reservoir flow problems. The two-dimensional, two-phase and problems. The two-dimensional, two-phase and two-dimensional, three-phase algorithms have been evaluated by several test problems and compared with the corresponding alternating direction iterative routines. The strongly implicit procedure (SIP) has been found to have several advantages in the solution of reservoir problems. It is fast, and in problems with extreme anisotropy in the transmissibilities and/or highly irregular geometries it can obtain a solution where the alternating direction procedure many times cannot. For the problems tested, it bas been found that a reliable set of iteration parameters is easily calculated from the coefficient matrix. Finally, SIP appears to be relatively insensitive to the rounding errors inherent in machine computations. Introduction The efficient solution of multidimensional reservoir problems involving the flow of two- or three-fluid phases is essential in petroleum reservoir simulation. Because of nonlinearities and generally complex geometries and boundary conditions, analytic solutions of the differential equations are at present impossible. One must, instead, seek solutions of the finite difference approximations of the equations through iterative techniques. Many iterative methods have been developed. Most of these, including relaxation and successive overrelaxation techniques, require excessive computer effort because they converge rather slowly or fail to converge. The more implicit alternating direction iteration procedure (ADIP) converges faster than the relaxation and overrelaxation schemes and, in general, requires less computational work. More recently, a new iterative technique has been developed. This technique is called the strongly implicit procedure, or simply SIP. It was demonstrated by Scone that SIP achieved greater rates of convergence than ADIP on all problems tested except the simple model problem in which the coefficients in the difference equation were constant and isotropic. Furthermore, the advantage of SIP over ADIP appears to increase as the complexity of the problem increases. SIP was originally developed and tested for the solution of a single equation in two-space dimensions. Its improved convergence over ADIP in this case led naturally to the development of SIP for the simultaneous solution of two or three coupled equations in two dimensions, such as arise in the simultaneous-solution approach to multiphase two-dimensional flow problems. SIP has also been extended to the solution of multiphase reservoir flow problems in three-space dimensions. The development and testing of the latter procedure is discussed elsewhere. In this paper, the SIP algorithms for two-dimensional problems are presented. The algorithms have been evaluated by presented. The algorithms have been evaluated by several test problems and compared with the corresponding ADIP routines. TWO DIMENSIONS: THE MULTIPHASE PROBLEM For purposes of generality, the system to be studied is comprised of coupled, two-dimensional parabolic equations. Employing this system will parabolic equations. Employing this system will facilitate investigation of any problem related to the two-dimensional flow of several fluids in a porous medium. porous medium. SPEJ P. 99

Unsteady Potential Flow Theory and Numerical Analysis of Forces on Cylinders Induced by Nearby Oscillating Disturbances

2009 ◽  
Author(s):  
Daniel T. Valentine ◽  
Farshad Madhi
Keyword(s):  
Numerical Model ◽  
Unsteady Flow ◽  
Potential Flow ◽  
Complete Solution ◽  
Boundary Integral ◽  
Circular Cylinders ◽  
Two Dimensional ◽  
Method Of Images ◽  
Surface Distribution ◽  
Flow Problems

The complete solution of several two-dimensional potential flow problems are reported that deal with the unsteady flow around circular cylinders. Three of the flows considered are induced by an oscillating disturbance near the cylinder. The three elemental disturbances examined are (1) a pulsating source, (2) a pulsating doublet and (3) a pulsating vortex. The formulas for the force acting on the cylinder due to each of the elemental disturbances were derived by applying the method of images and checked by deriving the equivalent surface distribution of sources to model the cylinder starting with Green’s second identity. The theory helped direct the development of a boundary-integral numerical model described and applied in this paper to solve the unsteady flow around a circular cylinder due to an arbitrarily specified oscillatory disturbance near the cylinder. The numerical method is validated by comparing predictions of the force with the exact solutions.

Approximate Numerical Solutions for Two-Dimensional Potential Flow Problems

1978 ◽  
Vol 100 (1) ◽  
pp. 122-124 ◽  
Author(s):  
A. Kieda ◽  
H. Yano
Keyword(s):  
Numerical Method ◽  
Surface Pressure ◽  
Potential Flow ◽  
General Class ◽  
Numerical Solutions ◽  
Two Dimensional ◽  
Weighted Residuals ◽  
Flow Problems ◽  
Pressure Distributions ◽  
Method Of Weighted Residuals

An approximate numerical method is proposed for solving two-dimensional potential flow problems. The method is included in the general class of “Method of Weighted Residuals.” Typical computed results are presented for the surface pressure distributions on an airfoil and single noncircular cylinders immersed in a uniform infinite stream.

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