Method integro-interpolation

The integro-interpolational method for constructing homogeneous difference schemes. Various physical processes (heat conduction or diffusion, vibrations, gas dynamics, etc.) are well-characterized by some integral... 

In Section 3.2 the integro-interpolational method was aimed at constructing the homogeneous conservative scheme (16) with the coefficients a, d and special form (15), namely with pattern functionals such that... 

The integro-interpolational method (IIM). In Section 2 we have already studied the IIM, but its possibilities and potential have not been illustrated in full measure. Here we consider other ways of its applications by appeal to the problem... 

Let us stress that the integro-interpolational method is a rather flexible and general tool in designing difference schemes relating to stationary and nonstationary problems with one or several spatial variables. 

Such an approximation is the result of a natural generalization of homogeneous conservative schemes from Chapter 3 for one-dimensional equations to the multidimensional case. These schemes can be obtained by means of the integro-interpolational method without any difficulties. 

By means of the integro-interpolation method it is possible to construct a homogeneous difference scheme, whose design reproduces the availability of the heat source Q of this sort at the point x = /. This can be done using an equidistant grid u)j and accepting / = x -f Oh, 0 <0 < 0.5. Under such an approach the difference equation takes the standard form at all the nodes x [i n). In this line we write down the balance equation on the segment x,j. 

Equations of gas dynamics in integral form are aimed at designing conservative difference schemes by means of the integro-interpolation method ... 

Further comparison of (40) with (27) shows that a new family of fully conservative schemes is contained in family (25)-(27) of describing conservative schemes with four parameters as a result of employing the integro-interpolation method. 

It should be emphasized that averaging technique does not require the grid to be small compared to the layering. These results can be considered as an outgrowth of the integro-interpolation finite-difference schemes. This term first appeared in the Russian literature in the papers of Tikhonov and Samarsky in the 1960 s (in Western literature the closest related technique is called the external approximation). However, only conformal variations of conductivity were treated in the classical integro-interpolation method. 

The first step during the course of the integro-interpolation method is to rely on the balance equation, say in the rectangle 0 < e < = 0.5/).,... 

Thus, the study of two-phase flows in diffuser-confusor devices can provide us with reliable results, based on the interpenetrating continuum model (the Euler approach). The numerical solution of the partial derivatives of the differential equations in the C-e turbulence model, using the implicit integro-interpolation finite volume method, provides us with the following fields of functions for a diffuser-confusor reactor axial u and radial v rates for each of the phases pressure p volume fractions of continuous and dispersed phases specific kinetic energy of turbulence k and its dissipation s, as well as some other characteristics. 

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