Integrated Computation of Finite Time Lyapunov Exponent During ...

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Efficient composition of evolving FTLE fields Evolve time h flow maps during the simulation, store them on hard disk, construct time T flow maps as needed Approximate reconstruction of Φ t 0+2h+T t 0 +2h Approximate reconstruction of Φ t 0+h+T t 0 +h Approximate reconstruction of Φ t 0+T t 0 }Fwd. time constructions Exact Φ t 0+T t 0 t 0 t 0 +h t 0 +2h . . . . . . t 0 +T-h t 0 +T t 0 +h+T t 0 +2h+T Simulation Time (t) Exact Φ t 0 t0 +T Approximate reconstruction of Φ t 0 t0 +T Approximate reconstruction of Φ t 0+h t 0 +h+T }Bkwd. time constructions Approximate reconstruction of Φ t 0+2h t 0 +2h+T Finn & Apte FTLE & DNS Integration 8
Computational flow of the integrated computations Main Flow Solver • t n+1 = t n + dt • Advance u n to u n+1 Update time h flow maps • Advance time h Lagrangian tracers (fwd) • Advance time h Eulerian fields (bkwd) u n+1/2 mod (t n+1 , h) ≠ 0 • Handle flow map B.C. RETURN mod (t n+1 , h) = 0 FTLE Computation • Map current tracer positions to launch cells to obtain time h forward flow map • Write time h flow maps to disk • Construct time T flow maps from sequence of N time h flow maps • Compute FTLE fields • Re-initialize time h flow maps on fixed grid. Block diagram showing the flow of the FTLE/DNS integration. Finn & Apte FTLE & DNS Integration 9
Page 1 and 2: Integrated Computation of Finite Ti
Page 3 and 4: Main Goal: Enhance DNS capability T
Page 5 and 6: Main Goal: Enhance DNS capability T
Page 7 and 8: Definition and typical computation
Page 9 and 10: Definition and typical computation
Page 11 and 12: The flow solver Originally develope
Page 13 and 14: Computing the forward time flow map
Page 15: Efficient composition of evolving F
Page 19 and 20: Moving Boundaries: Inline Oscillati
Page 21 and 22: Complex configurations: Flow throug
Page 23 and 24: Conclusions 1 We can compute evolvi
Page 25 and 26: Physica D: Nonlinear Phenomena, 149
Page 27 and 28: Double Gyre flow: [Solomon and Goll
Page 29 and 30: Double Gyre flow: [Solomon and Goll

Integrated Computation of Finite Time Lyapunov Exponent During ...

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