Class SpaldingLawOfTheWall

Inheritance Relationships

class SpaldingLawOfTheWall : public LawOfTheWall 

The law of the wall proposed by Spalding.

\[ y^+ = u^+ + \exp(-\kappa B) \left( \exp (\kappa B) - 1 - \kappa u^+ - \frac{1}{2}(\kappa u^+)^2 - \frac{1}{6}(\kappa u^+)^3 \right) \]

Since the formula above is differentiable, it is advised to use Newton’s method to solve for \(u_\tau \).

Usage:

    Law
    {
        type      Spalding;
        kappa     value; (default 0.4)
        B         value; (default 5.5)
    }

Reference:

        Spalding, D. B. (1961).
        A single formula for the 'law of the wall'.
        Journal of Applied Mechanics,
        28(3), 455-458.

Contributors/Copyright: 2016-2019 Timofey Mukha 2017 Saleh Rezaeiravesh

Source files

Public Functions

SpaldingLawOfTheWall(const word &lawname, const dictionary&): Construct provided TypeName and dictionary.

SpaldingLawOfTheWall(const scalar kappa, const scalar B): Construct from model constants.

SpaldingLawOfTheWall(const SpaldingLawOfTheWall&) = default: Copy constructor.

SpaldingLawOfTheWall &operator=(const SpaldingLawOfTheWall&) = default: Assignment.

virtual void printCoeffs() const override: Print the model coefficients to terminal.

virtual scalar value(const SingleCellSampler &sampler, label index, scalar uTau, scalar nu) const override: Return the value of the implicit function defining the law.

virtual scalar derivative(const SingleCellSampler &sampler, label index, scalar uTau, scalar nu) const override

Return the value of the derivative of the implicit function.

defining the law.