1 Introduction

The precision of fluid flow parameters values influences profoundly simulat ion processes out come. The calculated values of pressure, flow rate, and temperature may be distorted by imprecise values of parameters such as friction factor or heat transfer coefficients. Thus, a proper estimation of these parameters is of great importance to the numerical simulation of the flow. Both the friction factor and the heat transfer coefficients are very difficult to measure; therefore, their values can only be assessed by solving un inverse problem (i.e. parameter identification process). Since, the parameter estimation procedure, described and used in this report, requires multiple solution of inviscid gasdynamics differential equations describing the gas flow through the pipeline system, a multidomain solution method (MD) has been applied to solve efficiently the parameter identification problem.

2 Mathematical Model (Governing Equations)

This section describes the mathematical model equations for fluid flow and heat transfer used in the computer program PI (Parameter Identification - described in section 3), including source terms containing unknown parameters: friction factor and heat transfer coefficient to be determined (identified.) The basic set of equations describing an unsteady laminar flow comprises equations for conservation of mass and momentum and, in the case of nonisothermal flow, energy. For inviscid flow they are called Euler equations.

3.2 Problem Size and Options

The problem size is determined by the number of subdomains and their subdivisions. Since the size of the auxiliary matrix depends linearly on numbers of subdomains, it adds only negligible amount of computer space requirement (less than 1OK for a few hundreds of subdomains.) The main contributor to the size of the problem is the number of grid points alloted to the network under consideration. This number depends on required refinement and network topology. By using MD [I] method the network topology influence has been eliminated entirely because, unlike commonly used methods, the resulting solution matrix is of block-tridiagonal structure and its size is a linear function of grid number only. Such a size should not cause a problem for a workstation when MD method is applied. Remark: It is noteworthy, that the calculation time can be reduced in the future by the factor of processors number when applying the MD method in the parallel computation mode. Moreover, the computational space requirement is reducable, in the parallel mode, to the size of the biggest subdomain. The following Figure 2 shows indistinguishable agreement between these solutions and numerical ones when using a two point stencil compact scheme with twenty grid points in each of the subdomains. In addition, the pictures show an excellent match of "pressure" equalities at nodal points. The same conclusion can be drawn about solutions for U, and u, functions that influence directly the determination of sought parameter cx The convergence of a values to the true value of 1.2 and 0.6 is shown by the upper left pictures in Figures 2 and 3. As one can witness, the quality of a grid resolution influences the solution precision.

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