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

TL;DR

This paper introduces a parallel algorithm using OpenMP for solving the nonlinear heat equation in complex cylindrical domains, aiding the design of cryogenic devices with improved simulation efficiency.

Contribution

It presents a novel parallel implementation of the ADI method with adaptive time-stepping for nonlinear heat equations in multilayered cylindrical geometries.

Findings

Parallel algorithm achieves efficient simulation performance.

Adaptive time-step ensures convergence of the iterative method.

Performance aligns with existing literature case studies.

Abstract

In this article we present a parallel algorithm for simulation of the heat conduction process inside the so-called pulse cryogenic cell. This simulation is important for designing the device for portion injection of working gases into ionization chamber of ion source. The simulation is based on the numerical solving of the quasilinear heat equation with periodic source in a multilayered cylindrical domain. For numerical solution the Alternating Direction Implicit (ADI) method is used. Due to the non-linearity of the heat equation the simple-iteration method has been applied. In order to ensure convergence of the iteration process, the adaptive time-step has been implemented. The parallelization of the calculation has been realized with shared memory application programming interface OpenMP and the performance of the parallel algorithm is in agreement with the case studies in literature.