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19 May 2000 MIGAL for Phoenics 3.3 The New Coupled Algebraic Multi-grid Solver

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19 May HOURS !!!!

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19 May 2000 Which computer could run PHOENICS 5, 10 or 30 times faster ?

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19 May 2000 yours Yours

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19 May 2000 Yours with MIGAL 12 mn

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19 May 2000 Instead of SIMPLEST

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19 May 2000 The Problem Simple, Simpler, Simplec, Simplest, Piso are segregating algorithms Then they need under-relaxation to ensure stability of the velocity-pressure coupling (FALSDT) They are at least N 2 algorithm

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19 May 2000 SIMPLEST CPU

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19 May 2000 The Idea A better perfomance of the solver for each equation separatly IS NOT the solution We must solve implicitly the velocity-pressure coupling before accelerating with multi-grid

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19 May 2000 How ? Linearize the momentum equations but do not solve Build the continuity equation Solve the algebraic system composed of 3x3 or 4x4 blocs : A nb nb = S A nb = S = nb =

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19 May 2000 But... The CPU time cost per sweep increase (x10) Additional storage is needed (70 Mb for 100,000 3D cells) Mb/cellStaggeredCo-locative 2D4.E-43.E-4 3D7.E-45.E-4

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19 May D RAM

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19 May D RAM

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19 May 2000 RAM vs CPU : the Winning Bet

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19 May 2000 Library Cases 2D Lid-Driven Cavity Re=10,000

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19 May 2000 Library Cases 2D Lid-Driven Cavity Re=10,000 2D Flow Past a Flat Plate Re=10

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19 May 2000 Library Cases 2D Lid-Driven Cavity Re=10,000 2D Flow Past a Flat Plate Re=10 2D Flow in Unit of Staggered Tube Bank

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19 May 2000 Library Cases 2D Lid-Driven Cavity Re=10,000 2D Flow Past a Flat Plate Re=10 2D Flow in Unit of Staggered Tube Bank 2D Laminar Backward Facing Step

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19 May 2000 Library Cases 2D Lid-Driven Cavity Re=10,000 2D Flow Past a Flat Plate Re=10 2D Flow in Unit of Staggered Tube Bank 2D Laminar Backward Facing Step 2D Turbulent Backward Facing Step

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19 May 2000 Library Cases 2D Lid-Driven Cavity Re=10,000 2D Flow Past a Flat Plate Re=10 2D Flow in Unit of Staggered Tube Bank 2D Laminar Backward Facing Step 2D Turbulent Backward Facing Step 3D Flow Around a Group of Building

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19 May 2000 Library Cases 2D Lid-Driven Cavity Re=10,000 2D Flow Past a Flat Plate Re=10 2D Flow in Unit of Staggered Tube Bank 2D Laminar Backward Facing Step 2D Turbulent Backward Facing Step 3D Flow Around a Group of Building 3D Lid-Driven Cavity Re=1,000

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19 May D Lid-Driven Cavity Re=10,

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19 May D Cavity CPU

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19 May D Cavity Speed-up

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19 May D Flow Past a Flat Plate Re=10 20x x x190

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19 May D Plate CPU

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19 May D Plate Speed-up

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19 May 2000 Flow in Symmetry Unit of Staggered Tub Bank Re=140 10x x x210

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19 May 2000 Tube bank CPU

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19 May 2000 Tube Bank Speed-up

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19 May 2000 Backward Facing Step Laminar Re=150

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19 May 2000 Bstep_L CPU

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19 May 2000 Bstep_L Speed_up

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19 May 2000 Backward Facing Step Turbulent Quick-Koren (65x30) Re = 50,000

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19 May 2000 Backward Facing Step (turbulent 65x30)

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19 May D Flow Around Buildings

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19 May 2000 Buildings CPU

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19 May 2000 Buildings Speed-up

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19 May D Lid-Driven Cavity Re=1,

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19 May D Cavity CPU

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19 May D Cavity Speed-up

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19 May 2000 How to use MIGAL for Phoenics ?

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19 May 2000 Activating MIGAL (1/2) Set large false time steps –relax(U1, falsdt, 1.E+10) –relax(V1, falsdt, 1.E+10) –relax(W1, falsdt, 1.E+10) Activate MIGAL for pressure-velocity –spedat(MIGAL, SOLVED1, c, HYDRO)

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19 May 2000 Activating MIGAL (2/2) Activate MIGAL for scalar variables –spedat(MIGAL, SOLVED3, c, SMOKE) Change default parameters –spedat(MIGAL, RELAX1, r, 0.9) –spedat(MIGAL, LITER3, i, 3)

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19 May 2000 Conclusion Coupled Multi-grid Method are already of great interest for 2D and 3D flows. and will be unbeatable in the future. MIGAL is boosting Phoenics with large speed- ups increasing with the number of cells.

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19 May 2000 Roadmap for MIGAL With an affordable PC under 2500$

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19 May

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