NUMERICAL MODELING OF A DYNAMIC PROCESS IN A TECHNICAL SYSTEM WITH A NON-CYLINDRICAL COMPUTATIONAL DOMAIN

Abstract

:  A numerical approach for modeling dynamic processes in technical systems with a variable computational domain is considered. The mathematical model is formulated as a hyperbolic partial differential equation in a non-cylindrical domain. The geometry of the domain is described by a time-dependent boundary, which makes the direct application of standard finite-difference schemes nontrivial. A uniform space-time grid is introduced, and a second-order finite-difference approximation is constructed for the differential equation. The stability condition associated with the explicit scheme is established by means of the standard energy approach. A test problem with a known analytical solution is used to estimate the numerical error. The influence of the spatial and temporal mesh parameters on the accuracy of the computed solution is investigated. The proposed computational procedure can be used as a basic numerical tool for the analysis of dynamic processes in technical systems with variable geometric characteristics.