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Scientific Computing and Numerics for PDEs

Join the course led by Professor Jari Hämäläinen to master the core principles of scientific computing specifically tailored for partial differential equations (PDEs). Students will explore fundamental equations governing mass and heat flow, electric fields, and turbulence, while gaining hands-on experience with professional software tools like ANSYS and openFOAM. The course emphasizes implementing advanced numerical algorithms, including the Finite Difference Method (FDM) and Finite Element Method (FEM), through practical exercises and project assignments that connect to ongoing research at the CEID Centre.

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Scientific Computing and Numerics for PDEs

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  1. Scientific Computing and Numerics for PDEs Jari Hämäläinen Director, the CEID centre Professor, Industrial Mathematics www.lut.fi/ceid

  2. Course facts • “The student knows basic equations of mass and heat flow, physics of electric fields, acoustics, radiation and is able of use physical principles and conservation laws to model multi-physical systems and behaviour of materials, describe boundary conditions and choose ways to describe turbulence and multi-scale phenomena. The student is able to implement advanced numerical algorithms for the solutions and work with professional software tools.” • Theory: PDEs and numerical methods (FDM, FEM) • Exercises: Math exercises and numerical algorithms (e.g. Matlab) • Training: Working with software (ANSYS, Abaqus, openFOAM, Elmer) • The course is connected to the projects in the CEID centre and presents methods of scientific computing and software tools used in CEID projects • The Renewtech project on CFD in wind energy • New projects at LUT Savo (Varkaus) on forest, energy, automation, machinery – “PEAK” (=Puu, Energia, Automaatio, Konepaja) • Evaluation of open source CFD software like Elmer and OpenFOAM

  3. Renewtech LUT/CEID • Large-Eddy Simulation for atmospheric boundary layer • Modelling of forests and lakes • Efficient wind analysis tools • Aerodynamics of wind turbine blades with some defects • Multi-objective optimization of wind turbines w.r.t. energy, economy, noise, mechanics • International networking within ERCOFTAC

  4. Modelling in Multiple Scales J.Hämäläinen et al., J.Eng.Math. (2011)

  5. Finite Element Method (FEM) in Computational Fluid Dynamics (CFD) • Stabilized FEM for CFD, utilized e.g. in Elmer (Finnish text book, CSC, 2006) • New book “Handbook of Finite Element Methods for Computational Fluid Dynamics”, Hämäläinen, Kuzmin, SIAM, (coming in 2015) • In-house CFD software for optimal shape design and optimal control of the paper machine headbox, e.g. HOC Fibre software

  6. Course facts • Teachers • Jari Hämäläinen, weeks 10, 14, 15, 17 • PDEs in continuum mechanics • Finite Element Method (FEM) for Computational Fluid Dynamics (CFD) • Joonas Sorvari, weeks 11-13 • Basic numerics for PDEs, Finite Difference Method • Course assistant: Oxana Agafonova • Lectures and exercises • Lectures 14 h (6323) • Exercises 12+12 h (math + computer) (1528, 1546) (no March 6!) • Project assignment 40 h • Self study 40 h, exam and preparation 10 h • Total 134 h • Evaluation: exam (0-5), project work (pass/fail) • Math exercises will upgrade your final grade for one grade at maximum

  7. Exercises • Exercise questions will be published in noppa every Tuesday, and will be related to the last lecture (that is, the same Tuesday lecture) • Answers on exercise questions have to be send to Oxana by email exercises.lut@gmail.com on next Tuesday 12 pm at latest • All the exercises will be discussed then in class on Thursday • Visiting classes is not obligatory • Solutions have to be typed in MS Word, LibreOffice or Latex and saved in pdf • Also the problem statement, pictures of Matlab output should be included in report • Note: • some of questions will be given on exam • Math exercises will upgrade your final grade for one grade at maximum

  8. Project assignment • Working with software tools • ANSYS, openFOAM, Elmer, Abaqus • Team work, work load about 40 hours/person • Outline • Scientific background of the problem – literature review • Analytical solutions based on e.g. Bernoulli equations if possible • Modelling work with software • Sensitivity of the results w.r.t. grid density, inputs, etc. • Reporting • Work time report (hours used to the work) • Presentation on the results • Course assistant helping in the computer exercises • Computer exercises on Wednesdays in 1546 (at 8-10) • By appointment with Jari, Joonas or Oxana

  9. Geometry Physics Mesh Solve Reports Post-Processing Select Geometry Heat Transfer ON/OFF Unstructured (automatic/ manual) Steady/ Unsteady Forces Report (lift/drag, shear stress, etc) Contours Geometry Parameters Compressible ON/OFF Structured (automatic/ manual) Iterations/ Steps XY Plot Vectors Domain Shape and Size Flow properties Convergent Limit Verification Streamlines Viscous Model Precisions (single/ double) Validation Boundary Conditions Numerical Scheme Initial Conditions

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