Pavel Kus

Multiphysics field analysis and multiobjective design optimization: a benchmark problem

A magneto-thermal inverse problem, dealing with the optimal design of an induction heating device, is proposed as a benchmark. The coupled-field problem is analysed by means of a higher order finite element method. Then the optimal design problem is solved in terms of the Pareto front trading off two conflicting objective functions.

Finite-Element 2-D Model of Induction Heating of Rotating Billets in System of Permanent Magnets and its Experimental Verification

An alternative way of induction heating of nonmagnetic cylindrical billets is modeled. The billet rotates in static magnetic field generated by permanent magnets. The mathematical model of the process consisting of two second-order partial differential equations describing the distributions of magnetic and temperature fields is solved numerically in the quasi-coupled formulation. The computations are carried out by a fully adaptive higher order finite-element method that is implemented in own codes Agros2D and library Hermes. The most important results are verified experimentally on a prototype device built in our laboratory.

Hermes2D, a C++ library for rapid development of adaptive hp-FEM and hp-DG solvers

In this paper we describe Hermes2D, an open-source C++ library for the development and implementation of adaptive higher-order finite element and DG solvers for partial differential equations (PDE) and multiphysics coupled PDE problems. The library is suitable for applications ranging from simple linear PDE solvers to time-dependent solvers for nonlinear multiphysics coupled problems with dynamically changing meshes. We cover several typical application scenarios, and give a brief overview of methods and algorithms that the library provides. Numerical examples are provided.

Solution of 3D singular electrostatics problems using adaptive hp‐FEM

Purpose – This paper seeks to describe the solution of a simple electrostatic problem using an adaptive hp‐FEM and to show the benefits of this approach. Numerical experiments are presented to demonstrate its superiority.Design/methodology/approach – Adaptive hp‐FEM is used. In contrast with standard FEM, the automatic adaptivity procedure can choose from a variety of refinement candidates. An element with over estimated error can be refined in space, or its polynomial degree can be increased. Arbitrary level hanging nodes are allowed, so that no unnecessary refinements are performed in order to keep a mesh regular.Findings – Numerical solution of a singular electrostatic problem is presented. From the comparison it can be seen that the hp‐FEM outperforms both the standard linear and quadratic elements significantly. The accuracy of an hp‐FEM solution would be hard to attain by standard means due to the limited capacity of the computer memory.Originality/value – The paper describes results obtained from a...

Hard-coupled modeling of induction shrink fit of gas-turbine active wheel

Hard-coupled model of induction heating of a ferromagnetic disk is presented. The problem is described by three coupled partial differential equations (for the distribution of electromagnetic field, temperature field and field of thermoelastic displacements) whose coefficients are temperature-dependent functions. The system is solved numerically in the monolithic formulation by a fully adaptive finite element method of higher order of accuracy implemented into own codes Hermes and Agros2D. The methodology is illustrated by a typical example — heating of an active wheel of a high-speed gas turbine that is to be hot-pressed on a shaft with the aim of obtaining a shrink fit. The results are evaluated and discussed.

Model-based determination of nonlinear material parameters of metals with low melting points

An alternative way of determining the temperature-dependent characteristics of metals is presented. The method that is relatively simple and cheap is suitable mainly for metals with lower melting points. The paper starts with the experimental investigation of the melting process of the Field metal in an induction furnace, which provides all necessary information for determining the above material characteristics. These data are then used for a coupled numerical simulation of the process of heating and melting and also for sensitivity analysis and model-based determining of specific heat capacity. The results are again verified by measurements, with a very good agreement.

Optimized arrangement of device for electrostatic separation of plastic particles

Shape optimization of a device for electrostatic separation of triboelectrically charged plastic particles is carried out. The objective function maximizes the efficiency of separation consisting in the highest possible number of particles falling down to the prescribed bins. Electric field in the system is solved numerically, using the fully adaptive higher-order finite element method. The movement of particles in the device influenced by the Coulomb force is determined by means of an adaptive Runge-Kutta-Fehlberg method with a time varying time step. The shape optimization is carried out using a technique based on higher-order conjugate gradients. The methodology is illustrated by an example whose results are discussed.