![∂u ∂u ∂u
---+ Vx ---+ Vy ---= 0,
∂t ∂x ∂y
u(x,y;t = 0) = sin(κx )cos(κy ),
u(xb = [− 1,1],yb;t) = periodic,
u(xb,yb = [− 1,1];t) = sin(κ(x− Vxt )) cos(κ(y − Vyt)),](Imperial-NektarWorkshop1x.png)
The problem we want to run consists of a given initial condition (which depends on x and y) travelling in the x-direction at a constant advection velocity. To model this problem we create a computational domain also referred to as mesh or grid (see section 1.3) on which we apply the following two-dimensional function as initial condition and periodic as well as time-dependent Dirichlet boundary conditions at the mesh boundaries
|
| (1.2) |
where xb and yb represent the boundaries of the computational domain (see section 1.4), Vx = 2,Vy = 0 and κ = 2π.
We successively setup the other parameters of the problem, such as the time-step, the time-integration scheme, the I/O configuration, etc. (see section 1.4). We finally run the solver (see section 1.5) and post-process the data in order to visualise the results (see section 1.6).