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Extra resources for Beam Dynamics Issues for 1 TeV Linear Collider

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We believe that the main task in the problem of ‘optimum ADS’ is the task of algorithmic facilities for ADS (for example, the Boeing 50 Computing models and methods company carried out a thorough analysis of the results of approximately 700 calculation studies carried out on computers in the 70s and 80s; it was found that 70% of the final calculation results were inaccurate because of the application of inadequate mathematical models). Thus, the development of mathematical models and, on the basis of these models, of intellectual expert systems (IES) and the mechanics of solids, medicine, etc.

Complexity of equations The deep penetration of numerical methods into the mechanics of solid media and plasma physics is also explained by the fact that 49 Turbulence: New Approaches the equations, describing the phenomena taking place here, represent the most complex (in comparison with other areas of mathematical physics) system of integral differential equations in partial derivatives. In a general case, this is a nonlinear system of the mixed type with the unknown form of the transition surface (where the equations change their type) and ‘moving boundaries’: the boundary conditions of the problem are defined on surfaces or on lines which themselves are determined during calculations.

Using the proposed method of direct numerical modelling, it is possible using the ‘smoothed’ equations to determine the spatialtime structures of the dynamics of large vortices and by statistical processing of the pulsation-nonstationary regime determine their average ‘fluctuation’ characteristics: Reynolds stresses and turbulent energy (the correctness of this process is discussed below). 7. The numerical examination of the nominal-turbulent transition is carried out on the basis of complete Navier–Stokes equations.

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