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The Quest for Discrete Convection

The Quest for Discrete Convection. Dedicated to Piet Wesseling Arthur Veldman. Delft 1984 - 1990. Roommate CFD. Part-time appointment in Delft One day / week behind extra desk in Piet’s office. CFD class - first year. CFD is all about convection Only a first-order derivative, but …

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The Quest for Discrete Convection

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  1. The Quest for Discrete Convection Dedicated to Piet Wesseling Arthur Veldman

  2. Delft 1984 - 1990

  3. Roommate CFD • Part-time appointment in Delft • One day / week behind extra desk in Piet’s office

  4. CFD class - first year CFD is all about convection Only a first-order derivative, but … Standard model problem Pe large, e.g. 500 exact discrete (uniform)

  5. Adapted grid Solution has boundary layer  uniform grid gives not enough resolution Remedy: Adapt grid to physics, and everything should work fine … (?) … and indeed (!) original graph (1985)

  6. During lunch time With the CFD class going so well … chasing monsters and crooks … flight instruction by Piet CRASH!!! Next time lower your gear …

  7. CFD class - second year • Plenty of time to make ‘nice’ pictures • I wrote new program (old one got lost), • chose a ‘good’ grid, and … • Last year’s result was much better !!! • Where did I make the mistake??

  8. Once more … • Start with Taylor series • Combine these such that truncation terms • cancel and obtain the discrete convection • Check whether code is correctly implemented Alas! Everything was OK – except solution …

  9. In despair … What did I do last year? Did I betray my students? • First time is always race against time: • - no time for complicated arithmetic • - probably took simplest option Anxious for the result … Relief …

  10. What is the difference?

  11. What is the magic? • Term on diagonal that can have both signs • diagonal may be ‘destroyed’  eigenvalues can move to unstable half-plane no  ! 0 No contribution to diagonal; skew-symmetric! Together with stable diffusive contribution coefficient matrix is stable and non-singular

  12. Conservation of energy

  13. In practice Symmetry-preserving method is highly forgiving w.r.t. grid irregularities

  14. Many years later …

  15. Simulation of turbulent flow Leonardo Da Vinci Direct Numerical Simulation • Many flow details  fine grid required • Higher-order discrete convection

  16. Channel flow Re = 5600 mean flow

  17. Channel - turbulence Grid coarsening: 96  16 across channel Turbulent statisticsu’u’ * Only 8 points across boundary layer!

  18. Epilogue • Since 1992, Piet and I have 7 times • given the JMBC PhD-course CFD I • The quest in Piet’s TUD office led • to one of our main messages: • Discrete convection should not mess around with energy

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