Frantisek Mach

Numerical solution of coupled problems using code Agros2D

New code Agros2D for 2D numerical solution of coupled problems is presented. This code is based on the fully adaptive higher-order finite element method and works with library Hermes2D containing the most advanced numerical algorithms for the numerical processing of systems of second-order partial differential equations. It is characterized by several quite unique features such as work with hanging nodes of any level, multimesh technology (every physical field can be calculated on a different mesh generally varying in time) and a possibility of combining triangular, quadrilateral and curved elements. The power of the code is illustrated by three typical coupled problems.

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.

Higher‐order finite element modeling of rotational induction heating of nonferromagnetic cylindrical billets

Purpose – The purpose of this paper is to present a methodology of high‐precision finite element modeling of induction heating of rotating nonferromagnetic cylindrical billets in static magnetic field produced by appropriately arranged permanent magnets.Design/methodology/approach – The mathematical model consisting of two partial differential equations describing the distribution of the magnetic and temperature fields are solved by a fully adaptive higher‐order finite element method in the monolithic formulation and selected results are validated experimentally.Findings – The method of solution realized by own code is very fast, robust and exhibits much more powerful features when compared with classical low‐order numerical methods implemented in existing commercial codes.Research limitations/implications – For sufficiently long arrangements the method provides good results even for 2D model. The principal limitation consists in problems with determining correct boundary conditions for the temperature fi...

Model of Induction Heating of Rotating Non-Magnetic Billets and its Experimental Verification

Induction heating of non-magnetic cylindrical billets is modeled. The billet rotates in static magnetic field generated by appropriately distributed permanent magnets. The mathematical model of the process consists of two second-order partial differential equations describing the distributions of magnetic and temperature fields. Its solution is solved numerically in the quasi-coupled formulation respecting all important non-linearities. The computations are carried out by the code Agros2-D, based on a fully adaptive higher-order finite element method. Some results are verified experimentally on an industrial prototype of the device. Presented are also other important results obtained by measurements.

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.

Induction heating of cylindrical nonmagnetic ingots by rotation in static magnetic field generated by permanent magnets

Induction heating of cylindrical nonmagnetic billets by their rotation in static magnetic field is modeled. The magnetic field is produced by a system of appropriately arranged permanent magnets. The numerical model is solved by our own full adaptive higher-order finite element method in a monolithic formulation, i.e., both magnetic and temperature fields are solved simultaneously, respecting their mutual interaction. All principal nonlinearities are included in the model (permeability of ferromagnetic parts of the system as well as temperature dependences of physical parameters of the heated metal). The methodology is illustrated by two examples whose results are discussed.

Evolutionary algorithm-based multi-criteria optimization of triboelectrostatic separator

Abstract A device for electrostatic separation of triboelectrically charged plastic particles is modeled and optimized. Electric field in the system is solved numerically by a fully adaptive higher-order finite element method. The movement of particles in the device is determined by an adaptive Runge–Kutta–Fehlberg algorithm. The shape optimization of the electrodes is carried out by a technique based on genetic algorithm NSGA-II and also on simulated annealing.

Optimization of the system for induction heating of nonmagnetic cylindrical billets in rotating magnetic field produced by permanent magnets

The process of induction heating of cylindrical nonmagnetic billets is modeled and optimized. An unmovable billet is placed in rotating magnetic field generated by permanent magnets fixed in an external rotor driven by an asynchronous motor by means of a teeth gear. The coupled model of the problem consisting of two partial differential equations describing the distributions of magnetic and temperature fields in the system is solved by a fully adaptive higher-order finite element method. Computations are realized by own code Agros2D. The device is then optimized with respect to the total amount of heat generated in the billet; as the dimensions of the device are fixed, the only quantity that can be changed is the direction of magnetization of the individual permanent magnets. The optimization procedures represent a supplement to the code. Finally, the dynamic behavior of the optimized system is analyzed. The methodology is illustrated by a typical example whose results are discussed.

Modeling of rotational induction heating of nonmagnetic cylindrical billets

Induction heating of nonmagnetic cylindrical billets by rotation in uniform magnetic field produced by static permanent magnets is modeled. Numerical analysis of the process providing the distributions of magnetic and temperature fields is carried out in the monolithic formulation, using our own code based on higher-order finite element method. The methodology is illustrated by a typical example and the most important results are validated experimentally.

Advanced adaptive algorithms in 2D finite element method of higher order of accuracy

Purpose – The paper presents the principal elements of automatic adaptivity built in our 2D software for monolithic solution of multiphysics problems based on a fully adaptive finite element method of higher order of accuracy. The adaptive techniques are illustrated by appropriate examples.Design/methodology/approach – Presented are algorithms for realization of the h‐adaptivity, p‐adaptivity, hp‐adaptivity, creation of curvilinear elements for modelling general boundaries and interfaces. Indicated also is the possibility of combining triangular and quadrilateral elements (both classical and curved).Findings – The presented higher‐order adaptive processes are reliable, robust and lead to a substantial reduction of the degrees of freedom in comparison with the techniques used in low‐order finite element methods. They allow solving examples that are by classical approaches either unsolvable or solvable at a cost of high memory and time of computation.Research limitations/implications – The adaptive processe...