C. Pozrikidis, Boundary integral and singularity methods for linearized viscous flow, Cambridge Texts in Applied Mathematics. Cambridge University Press, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Abbreviated title. The Biharmonic Equation 1. Introduction. Boundary value problems for the biharmonic equation in two dimensions arise in the computation of the Airy stress function for plane stress problems [KK] Mik] Musk] and in steady Stokes flow of highly viscous fluids [MT, Chap. 22] [Poz]. Integral equations methods are a popular choice for the numerical solution of these equations [GGMa] MG] K, and references there] Poz] The application of conformal mapping to this problem, though classical, is less well known [KK] Musk] Unlike the Laplace equation, the biharmonic ....

....computation of the Airy stress function for plane stress problems [KK] Mik] Musk] and in steady Stokes flow of highly viscous fluids [MT, Chap. 22] Poz] Integral equations methods are a popular choice for the numerical solution of these equations [GGMa] MG] K, and references there] [Poz]. The application of conformal mapping to this problem, though classical, is less well known [KK] Musk] Unlike the Laplace equation, the biharmonic equation is not preserved under conformal transplantation. However, a biharmonic function and its boundary values can be represented in terms of ....

C. Pozrikidis, Boundary Integral and Singularity Methods for Linearized Viscous Flow, Cambridge U. Press, 1992.

....a microresonator packaged in the air is also presented, to show that the method can be used to analyze practical problems. Finally, in Section 6, we give conclusions and acknowledgments. FORMULATION In the frequency domain, the direct boundary inte gral equations for unsteady Stokes flow are [5] uj(xo) 1) 4rl [fi(x)Gij(i) Iui(x)Tik(i)nk(x) ds where S is the surface on the object in an infinite fluid, and the two Greens functions are given by [5] Gij(i ) aA(t) S( 2) OGij OGkj ( ijk( ik2 (X) 3) A = 2e U(1 R ) R (4) 6 = 2e ( 5) u = 6) In (1) ....

....and acknowledgments. FORMULATION In the frequency domain, the direct boundary inte gral equations for unsteady Stokes flow are [5] uj(xo) 1) 4rl [fi(x)Gij(i) Iui(x)Tik(i)nk(x) ds where S is the surface on the object in an infinite fluid, and the two Greens functions are given by [5] Gij(i ) aA(t) S( 2) OGij OGkj ( ijk( ik2 (X) 3) A = 2e U(1 R ) R (4) 6 = 2e ( 5) u = 6) In (1) uj(xo) is the jth component of the velocity vec tor at the source point Xo, f is the Stokeslet density function that corresponds to the surface traction, n is ....

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C. Pozrikidis, Boundary integral and singularity methods for linearized viscous flow, Cambridge University Press, Cambridge, 1992.

.... and viscous terms and solve the corresponding Stokes flow problem (linear) for an incompressible fluid [1] Due to the innately 3D nature of the devices and the complicated geometries involved, it is computationally advantageous to use a boundary integral formulation of the Stokes equations [2]. In ref. 1] a Fast Stokes solver was presented based on a precorrected FFT [3] acceleration of the boundary integral method. The computational complexity of the approach is O(nlog(n) where n is the number of panels used in the discretization of the surface of the device. This allowed the ....

....in this figure. 2 THE STOKES FLOW PROBLEM Let S represent the surface of the device (assumed rigid) on which the fluid drag force is to be computed. The indirect (first kind) formulation of the exterior Dirichlet problem corresponding to the incompressible Stokes flow equations is given by [2] vi(Xo ) 8 lsGij(Xo,x) f j(x) dS(X) i,j 1,2,3 . vi(x0) is the i tn component of the velocity vector (assumed known) at the source point x0 located on the surface of the device, fj(x) is the jtn component of the traction at the field point x also located on the surface of the device and ....

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C. Pozrikidis, "Boundary integral and singularity methods for linearized viscous flow", Cambridge University Press, New York t 992.

....to the Stokes problem, which is a vector problem. Before we touch the integral equations, let us briefly talk about Stokes flow and some key assumptions. 4. 1 The Stokes flow and the Stokes equations A viscous flow with a very small Reynolds number is called a Stokes flow or a creeping flow [13, 14, 24]. The Reynolds number is defined as Re = Uv , where U is the velocity, L is the characteristic length, and v is the kinematic viscosity of the fluid. The Reynolds number is frequently used to determine which is dominant between the inertia and the viscous effects, inertia force since Re oc . ....

....first. We assume there is a point force at 0in the free space with strength ( 0) The corresponding governing equations are: w. v:a g8 o) o V.t2 =0 (4. 3) 53 Solving the above equations yields the fundamental solutions of velocity, pressure, and stress tensor due to the point force [14, 24]: u, I Go. 2 o)g, 8r,u P( 8 P( o )g, X, Xo )g Go. o ) 4 , 2 : p, X,Xo) 7 Tk( 6 7 r= x0 . 4.4) 4.5) Note the repeated indices are Einstein summations. The stress cr of the fluid is defined as: Ou, Ou ] 4.6) and the surface force is f = n. Next, we ....

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C. Pozrikidis. Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge University Press, Cambridge, 1992.

....play a vital role in free surface flow simulations. One powerful attraction to these methods is ease of implementation: they are typically no more complex to implement on 3 D unstructured meshes than on 2 D structured meshes. 4. 5 Boundary Integral Methods Methods of the boundary integral type [53,73,141,146] can be highly accurate for modeling free surface flows, especially 2 D flows with relatively regular interface topologies. In this approach, the interface is explicitly tracked, as in moving mesh or front tracking schemes, but the flow solution in the entire domain is deduced solely from ....

C. Pozrikidis. Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge University Press, 1992.

....could play a vital role in mold filling simulations. One powerful attraction to these methods is ease of implementation: they are typically no more complex to implement on 3 D unstructured meshes than on 2 D structured meshes. Boundary Integral Methods Methods of the boundary integral type [52, 53] can be highly accurate for modeling free surface flows, especially 2 D flows with relatively regular interface topologies. In this approach, the interface is explicitly tracked, as in moving mesh or front tracking schemes, but the flow solution in the entire domain is deduced solely from ....

C. Pozrikidis. Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge University Press, 1992.

....a viscous fluid has also been treated using sophisticated analysis of ellipsoidal harmonics. For references on these works together with some perspectives on analytical and numerical techniques for Stokes flow past submerged bodies, the reader is directed to the standard monographs on the subject [10, 11, 12]. The singularity method, which was originated by Lorentz [13] has also been applied by many to consider the fluid motion about non spherical particles and Chwang and Wu [14] has exploited it further and gave references to previous works. Payne and Pell [15] treated the creeping flow problems of ....

C. Pozrikidis, Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge University Press, (1992).

....the Zimm model and previous simulation [22] To explore the anomalous scaling behaviour of the 2D MD data, we have to re examine the theory of a 2D polymer in a fluid. It appears that the unusual form of the hydrodynamic (Oseen) tensor Hnm in 2D has been overlooked in the past. It can be shown [27] that this is given by Hnm = 1 4j [ GammaI log (jRn Gamma Rm j) rnm rnm ] 9) where j is the viscosity and rnm is a unit vector from monomer m to n. The distance independence of the last term leads to an infinite range hydrodynamic interaction unique to 2D. The simplest way to predict ....

C. Pozrikidis, Boundary Integral and Singularity Methods for Linearized Flow (Cambridge University Press, London, 1992). p. 60.

....identity (2) for vector functions , OE. State the uniqueness theorem. Specify what do you mean by uniqueness. Hint: Find out a vector analog of the following scalar theorem used in electrostatics: If r Phi = 0, then Phi = const(r) References: Kim, Karilla] Exercise 2.1 and Sec. 2.2. 1, Pozrikidis] Sec. 1.5. Compare your findings with results obtained by other groups. Answer the guiding question. 3.5 Boundary conditions In Stokesian hydrodynamics from now on we will restrict to the stick boundary conditions, i.e. to the fluid velocity v(r) at the boundary equal to the rigid motion ....

.... are general, and which are due to the specific symmetries (no fluid motion at infinity) of the Oseen functions (14) 15) How does the unit vector n 0 point: out or into the fluid How do the equations simplify if there is no external forces acting on the fluid other than gravity Reference: Pozrikidis] Sec. 2.3, Kim, Karilla] Sec. 2.4.2, Happel,Brenner] Sec. 3.4. Eqs (20) 21) are valid if there is a closed boundary of any shape inside a fluid. How would you modify them to describe a rigid body in a fluid Explain. The integral representation (20) 21) still does not allow to address ....

C. Pozrikidis, Boundary integral and singularity methods for linearized viscous flow, Cambridge University Press 1992

....of Naval Research under Grant N00014 94 1 0310 and the National Science Foundation under grant DMS 9407030. c #1998 American Mathematical Society 137 138 H. D. CENICEROS AND T. Y. HOU methods is that they reduce the dimension of the problem by involving quantities along the interface only [34]. However, boundary integral methods designed for computing interface motion are very sensitive to numerical instabilities because the underlying problem is fairly singular. If left uncontrolled, these instabilities usually destroy the accuracy of the computations. Numerical instabilities have ....

C. Pozrikidis, Boundary integral and singularity methods for linearized viscous flow, Cambridge University Press, 1992. MR 93a:76027

....For axisymmetric geometries analytical solutions are presented by Davis [3] and Hasimoto [7] In their papers analytical formulations are given for flow over a circular hole in an infinitely thin plane wall. The analytical results of Davis are confirmed by the numerical computations of Pozrikidis [13, 14], who computed shear stress components in the neighborhood of a circular rim with a boundary integral method. SINGULARITIES AT RIMS IN THREE DIMENSIONAL FLUID FLOW 3 In this paper we derive analytical formulations for the solutions of the fluid flow equations in the neighborhood of a circular ....

C. Pozrikidis. Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge University Press, New York, 1992.

....t) v yy (x; y; t) F 2 (x; y; t) 1.1b) u x (x; y; t) v y (x; y; t) 0 (1.1c) Here u j (u; v) is the velocity vector, p is the pressure, is the viscosity, and F j (F 1 ; F 2 ) is the external force. We also use the notation x = x; y) below. See, for example, 3] 10] 19] 20] [42] for general discussions of Stokes flow. The equations (1.1) can be solved as a coupled system (as is done in [49] or alternatively reduced to a sequence of three Poisson problems, one for each variable. Differentiating (1.1a) with respect to x, 1.1b) with respect to y, and adding the equations ....

....is similar in spirit to our method. Boundary integral methods are also very popular for Stokes flow, since this linear problem can be reduced to an integral equation along the interface, reducing the dimensionality of the problem. For a description of this approach and some references, see e.g. [42]. This approach does not appear to extend to nonlinear problems such as the full Navier Stokes equations, however, whereas the Immersed Boundary Method does. We expect that our method can also be extended, and work is now underway to do so. 2. Representation of the interface and forces. The ....

C. Pozrikidis, Boundary Integral and Singularity Methods for Linearized Viscous Flow, Cambridge University Press, 1992.

.... in (24) has to be replaced by R 0 (t) 1 3sgn(A) 4 t 1 3 : 25) 4 Numerical Method The numerical method, which we use to follow the evolution of an axisymmetric bubble, is based on a boundary integral formulation for solving Stokes equations with a moving boundary [11] 2] [12]. The velocities of the bubble surface satisfy the Fredholm integral equation of the second kind, u j (x) P Z S u i (y)K ijk (x; y)n k (y)dS(y) f j (x) 26) where K ijk (x; y) 3 2 (y i Gamma x i ) y j Gamma x j ) y k Gamma x k ) jy Gamma xj 5 (27) f j (x) Z S (r Delta n(y) n ....

....reduced to line integrals by performing the azimuthal integration analytically. The resulting complete elliptic integrals of the first and second kind are computed by the recursive formulae [13] The numerical techniques of solving the system of equations is similar to those discussed in [14] 4] [12] [15] The bubble surface is approximated by a set of boundary nodes along the contour in the (r; z) meridional plane. All other values on the surface are obtained through the interpolation of a quintic spline [16] To solve (35) we apply the equation at the collocation point where the ....

C. Pozrikidis. Boundary integral and singularity methods for linearized viscous flow. Cambridge University Press, 1992.

....than existing techniques. 1 Introduction Boundary integral techniques provide a popular approach to studying free surface motion in liquids, covering a wide range of phenomena. Some examples are the propagation of waves in inviscid liquids [1] and the motion of drops in very viscous liquids [2]. One of the major features of boundary integral technique is that they provide an evolution equation for the motion of the interface explicitly. Since there is no need to determine the flow field away from the interface, the dimension of the problem is reduced by one. On the other hand, the ....

C. Pozrikidis. Boundary integral and singularity methods for linearized viscous flow. Cambridge University Press, 1992.

....distribution. Among several numerical methods, the boundary element method (BEM) is an elegant technique to solve linear dioeusion reaction equation (Brebbia and Dominguez (1989) Ramachandran (1993) In the recent past the BEM has found widespread use in AEuid dynamic problems (for example, Pozrikidis (1992), Power and Partridge (1994) But the method has not yet made an impact in the eld of chemical reaction engineering. Using BEM the dioeerential Equation (1) can be converted to an equivalent integral equation by applying the Green Gauss theorem. Owing to the integral nature of the resulting ....

Pozrikidis, C., Boundary integral and singularity methods for linearized viscous AEow, Cambridge University Press, Cambridge, (1992).

....Abbreviated title. The Biharmonic Equation 1. Introduction. Boundary value problems for the biharmonic equation in two dimensions arise in the computation of the Airy stress function for plane stress problems [KK] Mik] Musk] and in steady Stokes flow of highly viscous fluids [MT, Chap. 22] [Poz]. Integral equations methods are a popular choice for the numerical solution of these equations [GGMa] MG] K, and references there] Poz] The application of conformal mapping to this problem, though classical, is less well known [KK] Musk] Unlike the Laplace equation, the biharmonic ....

....computation of the Airy stress function for plane stress problems [KK] Mik] Musk] and in steady Stokes flow of highly viscous fluids [MT, Chap. 22] Poz] Integral equations methods are a popular choice for the numerical solution of these equations [GGMa] MG] K, and references there] [Poz]. The application of conformal mapping to this problem, though classical, is less well known [KK] Musk] Unlike the Laplace equation, the biharmonic equation is not preserved under conformal transplantation. However, a biharmonic function and its boundary values can be represented in terms of ....

C. Pozrikidis, Boundary Integral and Singularity Methods for Linearized Viscous Flow, Cambridge U. Press, 1992.

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C. Pozrikidis, Boundary integral and singularity methods for linearized viscous flow, Cambridge Texts in Applied Mathematics. Cambridge University Press, 1992.

No context found.

C. Pozrikidis, Boundary integral and singularity methods for linearized viscous flow, Cambridge Texts in Applied Mathematics. Cambridge University Press, 1992.

No context found.

C. Pozrikidis, Boundary Integral and Singularity Methods for Linearized Viscous Flows, Cambridge Univ. Press, New York, 1992.

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