OperatorsStandard Operators ( ): parenthesis (there is no limit in the number of nested parenthesis.) + : add - : subtract / : divide * : multiply ^ : power Special Operators @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)
(a and b can be any expression) Tip: Initial conditions are denoted by adding the suffix @t0 to the dependent variable name (e.g., U@t0) Tip: Boundary conditions are denoted by adding the suffix @xL or @xU to the variable name (e.g., U@xL) Tip: you can build logical constructs by using the > or < operators (e.g., (t > 10)*5 is 0 for time less than 10 and 5 for times greater or equal 10) |
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