Operators

( ): parenthesis (there is no limit in the number of nested parenthesis.)

+ : add

- : subtract

/ : divide

* : multiply

^ : power

@t0: Initial condition for any dependent variable (e.g., U@t0 = U(t=t0))

@xL: Lower boundary value of any variable with x-dependence (e.g., U@xL = U(x=xL))

@xU: Upper boundary value of any variable with x-dependence (e.g., U@xU = U(x=xU))

dx (u) : First spatial (x) derivative of any expression u with x-dependence. By default, first derivatives are approximated by a five point centered approximation. Other approximations are possible.

dxu (u,c): First upwind spatial (x) derivative of any expression u with x-dependence. By default, first upwind derivatives are approximated by a five point biased upwind approximation (smooth ends). Other approximations are possible. Upwind derivatives are recommended for strongly convective (hyperbolic) problems. c indicates the direction of upwind (a positive or negative value)

dxx (u,ab): Second spatial (x) derivative of any expression with x-dependence. By default, second derivatives are approximated by five point centered approximations. Other approximations are possible. ab denotes the type of lower and upper boundary condition. Possible values for a and b are D (for Dirichlet) and N (for Neumann.) Thus, ab could adopt the values of DD, DN, NN, or ND.

_t: time (t) derivative of any dependent variable. When used in the RHS, this operators denotes the t-derivative value of the variable to which is applied. When used in the LHS, this operator allows definition of the t-derivative expression in the RHS (e.g., u_t = 4*x means that the time derivative of u is equal to 4*x)

1. b: the result is the greater of a,b
2. a < b: the result is the smaller of a,b

(a and b can be any expression)

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