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Scientific Computing and Numerics for PDEs

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

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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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