sofia.pde.rkn.rkn

sofia.pde.rkn.rkn.rkn(F: dict[Field, sp.Expr], order: RK_ORDERS_OR_NAMES, dt: sp.Symbol, post: CodegenAST | None = None) → RKn

Return a Runge-Kutta update scheme of the given update expressions.

Parameters:

• F – Mapping of fields to their time derivative expressions. Each entry {u: expr} corresponds the equation du/dt = expr.

• dt – Symbol representing the timestep in any of the given expressions.

• order –

  Runge-Kutta order or scheme name. Supported values include:

  • Integer orders: 1, 2, 3, 4

  • Named schemes: “euler”, “midpoint”, “heun2”, “ralston2”, “kutta3”, “heun3”, “ralston3”, “SSPRK3”, “3/8”, “m2s2”

• post – Optional extra IR that should be appended to each RK stage. Any appearance of dt in this IR will be adjusted to the total timestep of the stage.

Returns:

IR token representing the Runge-Kutta integration scheme, which can be expanded by calling .doit().

Return type:

rkn_token