Course detail

Mathematical Modelling

FSI-PMMAcad. year: 2025/2026

Due to the development of computer technology, the numerical simulation has become helpful in designing and optimising foundry processes. Mathematical simulation is aimed at the tuning of the designed technology in the phase of production preparation in order to avoid expensive experimental testing. The simulation of foundry processes connects numerical methods, physics and computer technology. It enables the study of processes during melt flow, solidification and cooling of castings.

Language of instruction

Czech

Number of ECTS credits

Mode of study

Not applicable.

Guarantor

Ing. Vladimír Krutiš, Ph.D.

Department

Institute of Manufacturing Technology (ÚST)

Entry knowledge

Basic knowledge of Foundry technology, knowledge of liquid flows and heat transfer, basic computer skills

Rules for evaluation and completion of the course

Course – unit credit requirements-optimisation of real casting technology, participation in the lessons
Exam - written and oral parts
Participation in seminars is required. An apologized absence from seminars may be compensated by individual work.

Aims

The aim of the course is to explain all the stages of simulation preparation and to give a compact view of the possibilities of computer assisted systems in the area of foundry processes.


Student will acquire the knowledge of 3D modelling of castings, definition of initial and boundary conditions of numerical simulation, evaluation of simulation results. The optimisation of gating and feeding systems is done using real castings and is performed for all foundry processes (gravity sand and die casting, high pressure die casting, investment casting, semi-solid processes). Calculation of production costs and sale price of castings together with Pacyna’s classification of castings is described. Relationships between other modules for thermo-mechanical calculation of castings are shown. The calculations are carried out with the support of modern software products.

Study aids

The materials will be accessible via e-learning.

Prerequisites and corequisites

Not applicable.

Basic literature

BONOLLO, F., ODORIZZI, S. Numerical Simulation of Foundry Processes. 1st ed. Padova: S.G.E., 2001, 264 p. ISBN 88-86281-63-3
Nová, I.:Tepelné procesy ve slévárenských formách, TU Liberec, 2003 (CS)
Rappaz M., Dantzig A. : Solidification, 2nd edition. EPFL Press, 2016. ISBN 978-0-84938-238-3 (EN)

Recommended reading

Abhilash E., Joseph M. A.: Modelling and Simulation of Casting Process: an Overview, Indian Foundry Journal, Vol. 55, No.10, 2009, pp 28-37 https://www.researchgate.net/publication/270757498_Modelling_and_Simulation_of_Casting_Process_an_Overview) (EN)
Hattel JH, Pryds N, Thorborg J, Lipinski M, Schneider M, Hattel JH, (ed.).: Fundamentals of Numerical Modelling of Casting Processes. Polyteknisk Forlag, 2005. 540 p. (EN)
Herman, A. a kol.: Počítačové simulace ve slévárenství, Vydavatelství ČVUT, 2000

Classification of course in study plans

  • Programme N-SLE-P Master's 1 year of study, summer semester, compulsory

  • Programme C-AKR-P Lifelong learning

    specialization CLS , 1 year of study, summer semester, elective

Type of course unit

 

Lecture

13 hod., compulsory

Teacher / Lecturer

Ing. Vladimír Krutiš, Ph.D.

Syllabus

  1. Virtual Engineering - Introducing the Principles.
  2. The use of numerical simulation in the foundry industry - The objectives of the deployment of simulation.
  3. Basics of heat transfer in the metal-mould-surrounding system
  4. Numerical simulation methods.
  5. Definition of initial calculation conditions + thermo-physical data.
  6. Definition of calculation boundary conditions.
  7. Overview of simulated processes in the foundry industry.
  8. Post-processing and analysis of results.
  9. Evaluation criteria for solidification of castings - prediction of defects.
  10. Validation of numerical simulation of foundry processes.
  11. Examples of gravity casting in sand moulds.
  12. Die casting simulation (HPDC, LPDC).
  13. Investment casting simulation.

Computer-assisted exercise

26 hod., compulsory

Teacher / Lecturer

Ing. Vladimír Krutiš, Ph.D.

Syllabus

1. Geometry design - data import and export.
2. Preparation of surface and volume meshes.
3. Repairing of bad meshes.
4. Definition of initial and boundary conditions.
5. Calculation definition; modules, calculation steps.
6. Examples of gravity casting calculation.
7. Examples of pressure casting calculation.
8. Examples of investment casting calculation.
9. Calculation of special processes.
10. Porosity calculation.
11. Optimisation of gating and feeding systems.
12. Post-processing.
13. Results validation - examples from practice.