A particle-in-Burgers model: theory and numerics - Laboratoire de ...

Model and motivation Auxiliary steps Results h = 0: coupling h = 0: definition, uniqueness h = 0: numerics, existence The coupled problem
Coupled problem: a well-balanced random-choice numerical scheme
t
t n+1
t n
x
g0(u n In−1, u n In )
u n+1
In
u n uIn n In
ũ n+1
In
h n + v n ∆t
h n + y
gv n(un In ,ϕ− α(u n In+1))
xIn−1/2 h n = xIn+1/2
gv n(ϕ+ α(u n In ), un In+1)
u n+1
In+1
u n In+1
ũ n+1
In+1
g0(u n In , un In+1)
h n+1
xIn+3/2
Figure: Representation of the algorithm based on the well-balanced scheme.