solve_burgers_1d
Solve the 1D Burgers equation with explicit finite differences, using an initial expression and Dirichlet boundary values; returns downsampled results and saves the full grid.
Instructions
Solve u_t + uu_x = nuu_xx with explicit finite differences.
``u_x`` uses a centred difference and ``u_xx`` a second-order centred
difference. ``initial`` is an expression in x; the ends use the constant
Dirichlet values ``left`` and ``right``. The explicit scheme requires
dt <= dx^2/(2*nu) (diffusion) and dt <= dx/max|u| (CFL); a violation is
reported as an error with a hint to increase nt. The full (t, x) grid is
saved to .npz and returned downsampled to at most 20 space and 20 time
points.
Tool call template
Replace each placeholder with a value matching the input schema. Only required parameters are included; add optional parameters as needed.
{
"id": 1,
"jsonrpc": "2.0",
"method": "tools/call",
"params": {
"arguments": {
"nu": "<nu>"
},
"name": "solve_burgers_1d"
}
}Input Schema
| Name | Required | Description | Default |
|---|---|---|---|
| nt | No | ||
| nu | Yes | ||
| nx | No | ||
| left | No | ||
| right | No | ||
| t_end | No | ||
| length | No | ||
| initial | No | sin(pi*x) |