The regularized semi-Lagrangian Störmer-Verlet time ... - Met Office
The regularized semi-Lagrangian Störmer-Verlet time ... - Met Office
The regularized semi-Lagrangian Störmer-Verlet time ... - Met Office
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Semi-<strong>Lagrangian</strong> St örmer-<strong>Verlet</strong><strong>time</strong>-stepping<strong>The</strong><strong>regularized</strong><strong>semi</strong>-<strong>Lagrangian</strong>Stormer ¨ -<strong>Verlet</strong><strong>time</strong>steppingmethodSebastianReichIdeal fluid dynamics may be viewed as the motion of a continuumof “particles” with positions x(a, t). Hence the Eulerequations are equivalent to (<strong>Lagrangian</strong> formulation)DuDt = F := − 1ρM 2 p,DxDt = u.Formally apply the Störmer-<strong>Verlet</strong> method to the <strong>regularized</strong>formulation:u n+1 = u n + Δt F n+1/2 ,x n+1/2 = x n−1/2 + Δtu nwith1 F = −ρM 2 p.Linear stability requires α ≥ Δt/2.
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