Algorithm and simulation of heat conduction process for design of a thin multilayer technical device

Abstract

A model of a multilayer device with non-trivial geometrical structure and nonlinear dependencies of thermodynamic material properties at cryogenic temperatures is suggested. A considered device, called cryogenic cell, is intended for use in multicharged ion sources for pulse injection of gaseous species into ionization space of ion sources. The main requirement for the cryogenic cell operation is the permanent opening and closing for gaseous species injection in a millisecond range, while cell closing is provided by freezing of the gaseous specie at the outer surface of the cell and the cell opening -by the corresponding pulse heating of the cell surface up to definite temperature. The thermal behaviour of the device in a millisecond time range is simulated. The algorithm for solving the non-stationary heat conduction problem with a time-dependent periodical heating source is suggested. The algorithm is based on finite difference explicit-implicit method. The OpenCL realization of the algorithm is discussed. The optimal particular choice of the parameters to provide the required pulse temperature regime of the designed cryogenic cell for the chosen working gas is presented. Based on these results further optimization can be formulated.

Parallel algorithm for numerical solution of heat equation in complex cylindrical domain

“…The purpose of this work is to develop algorithms for simulation of the heat conduction process inside the so-called pulse cryogenic cell [1,2]. Such simulations are important for designing the cell that implements "the thermal gates" of a portion injection of working gases into the ionization chamber of a multiply charged ion source [3]. While reliable operation of mechanical valves for pulsed injection of gaseous mixtures in the millisecond range at cryogenic temperatures is practically impossible, the use of gas temperature properties at cryogenic temperatures can be a real alternative.…”

Effective Methods for Solving Band SLEs after Parabolic Nonlinear PDEs

“…Such a problem was solved in [1]. There, a finite difference scheme of first-order approximation was built that leads to a TD SLE with a diagonally dominant coefficient matrix.…”

“…In this note, we focus on solving pentadiagonal (PD) and tridiagonal (TD) systems of linear algebraic equations (SLEs) which are obtained after the discretization of parabolic nonlinear partial differential equations (PDEs), using finite difference methods (FDM) of second-order approximation. Such a problem was solved in [1]. There, a finite difference scheme of first-order approximation was built that leads to a TD SLE with a diagonally dominant coefficient matrix.…”

Performance Analysis of Effective Methods for Solving Band Matrix SLAEs After Parabolic Nonlinear PDEs

“…In [1], a finite difference scheme with first-order approximation of a parabolic PDE was built that leads to a TD SLAE with a diagonally dominant coefficient matrix. The system was solved using the Thomas method (see [2]).…”