Implicit-Explicit Runge-Kutta schemes for hyperbolic systems ... - utenti

Lattice-Boltzmann models
∂tf + v
ɛ · ∇xf = 1
ɛ 2 τ (f − f eq ), x, v ∈ R 2 ,
v ∈ {c0, . . . , cN−1}, N = 9, ci ∈ {(0, 0), (0, ±1), (±1, 0), (±1, ±1)}.
f eq �
[ρ, u](v) = ρ 1 + 3u · v − 3
2 |u|2 + 9
�
(u · v)2 f
2 ∗ (v),
ρ(x, t) =
N−1 �
i=0
f(x, ci, t), ρu(x, t) =
N−1 �
i=0
cif(x, ci, t),
f ∗ (c0) = 4
9 , f ∗ (ci) = 1
9 , i = 1, ..., 4, f ∗ (ci) = 1
, i = 5, ..., 8
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As ɛ → 0 we obtain the incompressible Navier-Stokes equations with Reynolds number
O(1/τ).
shear layer
(x, y) ∈ [0, 2π] 2 , ux(x, 0) = 0.05 sin(x), periodic b.c. and
uy(x, y) = tanh(15(y − π/2)/π), y < π, uy(x, y) = tanh(15(3π/2 − y)/π), y > π.
We test IMEX-SSP2(2,2,2) and IMEX-SSP3(3,3,2) schemes combined with second and
third order upwind schemes based on CWENO reconstructions.
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