Dual reciprocity

The pump consists of dual reciprocating pistons which are hydraulically controlled. Oil is distributed by the system to the two pistons which are 180° out of phase (as with the Altex and Waters systems). A fixed volume of hydraulic fluid is delivered to the control system for every revolution of a special gear pump. The latter is controlled by a motor having a constant speed and a tachometer feedback circuit. Other compensating circuits... 

In Chapter 11 of this book we will use the thin spline radial function to develop the radial basis functions collocation method (RBFCM). A well known property of radial interpolation is that it renders a convenient way to calculate derivatives of the interpolated function. This is an advantage over other interpolation functions and it is used in other methods such us the dual reciprocity boundary elements [43], collocation techniques [24], RBFCM, etc. For an interpolated function u,... 

P.W. Partridge, C.A. Brebbia, and L.C. Wrobel. The dual reciprocity boundary element method. Computational Mechanics, Southampton, 1991. 

Develop a Dual Reciprocity boundary-only integral equation for the Navier-Stokes system of equations. 

B.A. Davis, P.J. Gramann, J.C. Maetzig, and T.A. Osswald. The dual-reciprocity method for heat transfer in polymer processing. Engineering Analysis withBoundary Elements, 13 249-261, 1994. 

W.F. Florez. Multi-domain dual reciprocity method for the solution of nonlinear flow problems. PhD thesis, University of Wales, Wessex Institute of Technology, Southampton, 2000. 

W.F. Florez. Nonlinear flow using dual reciprocity. WIT press, Southampton, 2001. 

Viscous heating temperature rise due to a combined drag-pressure flow between two parallel plates. Using RFM, Estrada [4] computed the temperature rise of a fluid subjected to a combination of drag and pressure flow between parallel plates and compared the results of an anlytical and a boundary element dual reciprocity (BEM-DRM) solutions presented by Davis et al. [3], Figure 11.2 presents a schematic of the problem with dimensions, physical properties and boundary conditions. 

BEM) or using dual reciprocity method (which requires a set of additional collocation points defined in the solution domain). 

The BEM has been applied in scanning electrochemical microscopy applications by Fisher and Denuault [169] to examine the influence of probe and substrate surface topography. In addition, time-dependent phenomena have been assessed in oil droplets [170, 171] and a range of microelectrode geometries using the dual reciprocity method (DRM) [172] closely related to the BEM [173]. 

A way of eliminating the domain integral in Eq. 8.81 is based on the well-known idea of combining a particular solution to a complementary solution of a homogeneous problem. This idea was discussed in Buzbee et al. (1971), who named the method the capacitance matrix method. Brebbia and Nardini (1986) have applied the concept to boundary element method and called it the dual reciprocity method (DRM). Henry and Banerjee (1988) have also proposed a related method in the name of the particular integral method. Now, let us consider a particular solution T that satisfies... 

Figure 10 The primary components of the system shown in Fig. 9 include the control panel (upper left), injection mechanism (upper right), autosampler carousels (mid-level), independently driven dual reciprocating solvent delivery pistons (lower left), and degasser/solvent select module (lower right). 

Partridge PW, Brebbia CA, Wrobel LC (1992) The Dual Reciprocity Boundary Element Method. Elsevier, London... 

Fulian Q, Ball JC, Marken F, Compton RG, Fisher AC (2000) Volttimmetry of electroactive oil droplets. Part I numerical modeUing for three mechanistic models using the dual reciprocity finite element method. Electroanalysis 12 1012-1016... 

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