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71 lines
2.5 KiB
Python
71 lines
2.5 KiB
Python
#!/usr/bin/env python3
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"""CFL bound verification sweep for Burgers step correspondence."""
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import random, math, json, hashlib
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from datetime import datetime, timezone
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Q16 = 65536
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random.seed(42)
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def step(u, N, nu, dx, dt):
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nu_q = int(nu*Q16); dt_q = int(dt*Q16); dx_q = int(dx*Q16)
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new = [0]*N
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for i in range(N):
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ux = ((u[(i+1)%N] - u[(i-1)%N]) // (2*dx_q)) if i>0 and i<N-1 else 0
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uxx = ((u[(i+1)%N] - 2*u[i] + u[(i-1)%N]) // (dx_q*dx_q//Q16)) if i>0 and i<N-1 else 0
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ui = u[i]
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rhs = ((nu_q * uxx) // Q16) - ((ui * ux) // Q16)
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new[i] = u[i] + (dt_q * rhs) // Q16
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return new
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def kinetic_energy(u):
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return sum((v*v)//Q16 for v in u) // 2
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results = []
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for N in [4, 8, 16, 32]:
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for nu in [0.05, 0.1, 0.2]:
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for dt in [0.005, 0.01, 0.02]:
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max_err = 0; max_E0_val = 0
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for _ in range(25):
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u = [0]*N
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for i in range(1, N-1):
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u[i] = random.randint(-Q16//2, Q16//2)
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E0 = kinetic_energy(u)
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u1 = step(u, N, nu, 1.0, dt)
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E1 = kinetic_energy(u1)
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obs = abs(E1 - E0) / Q16
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max_err = max(max_err, obs)
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max_E0_val = max(max_E0_val, E0/Q16)
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cfl = round(dt * 2.0 * max_E0_val, 6)
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within = max_err < cfl + 0.001
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results.append({
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'N': N, 'nu': nu, 'dt': dt,
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'max_E0': round(max_E0_val, 4),
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'max_step_error': round(max_err, 6),
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'cfl_bound': cfl,
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'within_cfl': within,
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})
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receipt = {
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'schema': 'burgers_cfl_sweep_v1',
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'claim_boundary': 'monte_carlo_sweep;cfl_bound_verification',
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'results': results,
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'summary': {
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'total_cases': len(results),
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'all_within_cfl': all(r['within_cfl'] for r in results),
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},
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'computed_at': datetime.now(timezone.utc).isoformat(),
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}
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canonical = json.dumps(receipt, sort_keys=True, separators=(',', ':'))
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receipt['receipt_sha256'] = hashlib.sha256(canonical.encode()).hexdigest()
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with open('burgers_cfl_sweep_receipt.json', 'w') as f:
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json.dump(receipt, f, indent=2)
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for r in results:
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mark = "✓" if r['within_cfl'] else "✗"
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print(f"N={r['N']:2d} ν={r['nu']:.2f} dt={r['dt']:.3f} "
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f"E0max={r['max_E0']:6.2f} err={r['max_step_error']:.6f} "
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f"CFL={r['cfl_bound']:.6f} {mark}")
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print(f"\nAll within CFL: {receipt['summary']['all_within_cfl']}")
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print(f"Receipt: burgers_cfl_sweep_receipt.json")
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print(f"SHA256: {receipt['receipt_sha256']}")
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