Uses formulae from linear wavy theory.

Base classes

• public vtb::core::Linear_velocity_potential_solver_base< T >

Methods

• solve(const Grid< T, 4 > & grid_tzxy, const Array< T, 2 > & wavy_surface) -> voidvirtual

  Calculate velocity potential for each grid point.

  grid_tzxy

  Four-dimensional $(t,z,x,y)$ grid for each point of which velocity potential is calculated. This grid includes two-dimensional $(x,y)$ wavy surface grid for each point of which wavy surface elevation is given.

  
  

  wavy_surface

  two-dimensional $(x,y)$ surface elevation array

  
  

  Date

  2018-08-10

  Author

  Ivan Gankevich

• window_function(const Grid< T, 2 > & wngrid, const T z, Array2< T > & result) -> void
• Linear_velocity_potential_solver()
• window_function(const Grid< T, 2 > & wngrid, const T z, Array2< T > & result) -> void

  Computes window (first) function $\mathcal{W}$.

  • For infinite depth the formula is $$\mathcal{W}(\vec{k}) = \frac{\exp\left(|\vec{k}|\right)}{|\vec{k}|}.$$
  • For finite depth the formula is $$\mathcal{W}(\vec{k}) = \frac {\cosh\left(|\vec{k}|(z+h)\right)} {|\vec{k}|\cosh\left(|\vec{k}|h\right)}.$$

  Date

  2018-08-14

  Author

  Ivan Gankevich

• solve(const Grid< T, 4 > & grid_tzxy, const Array< T, 2 > & wavy_surface) -> voidvirtual

  Computes velocity potential $\phi$. The integration is implemented using FFT and is done over wave number range which is computed directly from the wavy surface.The main formula for velocity potential is $$\phi(x,y,z;t) = \mathcal{F}^{-1}_{x,y}\left\{ \mathcal{W}(u,v;z) \cdot \mathcal{F}_{u,v}\left\{\mathcal{S}(x,y;t)\right\} \right\},$$ where $\mathcal{W}$ is window function and $\mathcal{S}$ is second function. For details see documentation of the corresponding methods.

  Date

  2018-08-14

  Author

  Ivan Gankevich

  See

  window_function

  See

  second_function

• ~Linear_velocity_potential_solver()
• Linear_velocity_potential_solver()

Base class for linear velocity potential solver.

Base classes

• public vtb::core::Velocity_potential_solver< T, 3 >

Derived classes

• vtb::core::Linear_velocity_potential_solver< T, P >
• vtb::core::Linear_velocity_potential_solver_opencl< T >

Methods

• store_past_values(const Array< T, 2 > & zeta, const Grid< T, 2 > & grid) -> voidprotected
• second_function(const Grid< T, 4 > & grid_tzxy, Array< C, 2 > & result) -> void

  Computes second function.

  • For large-amplitude waves the second function is computed as $$\mathcal{S}(x,y,t) = \frac{\zeta_t(x,y,t)}{ i \left( \left(\zeta_x + \zeta_y\right)/s - \zeta_x - \zeta_y \right) - 1/s },$$ where $s=\sqrt{1 + \zeta_x^2 + \zeta_y^2}$.
  • For small-amplitude waves the second function is computed as $$\mathcal{S}(x,y,t) = -\zeta_t(x,y,t).$$

  Date

  2018-09-15

  Author

  Ivan Gankevich

Base class for all velocity potential solvers.

Fields

• Grid< T, 2 > _elevation_grid
• Array< T, 3 > _elevation
• Array< T, 3 > _potential

Methods

• clear() -> void
• operator()(const Grid< T, 4 > & grid_tzxy, const Array< T, 2 > & wavy_surface) -> void
• solve(const Grid< T, 4 > & grid_tzxy, const Array< T, 2 > & wavy_surface) -> voidvirtual

  Calculate velocity potential for each grid point.

  grid_tzxy

  Four-dimensional $(t,z,x,y)$ grid for each point of which velocity potential is calculated. This grid includes two-dimensional $(x,y)$ wavy surface grid for each point of which wavy surface elevation is given.

  
  

  wavy_surface

  two-dimensional $(x,y)$ surface elevation array

  
  

  Date

  2018-08-10

  Author

  Ivan Gankevich

• elevation() const -> const Array< T, 3 > &

  Get three-dimnesional wavy surface elevation field that includes past values.

• potential() const -> const Array< T, 3 > &

  Get velocity potential field.

• assumptions() const -> const Assumptions &
• assumptions(Assumptions rhs) -> void
• wave_number_grid() const -> const Grid< T, 2 > &
• wave_number_grid(const Grid< T, 2 > & rhs) -> void
• depth(T rhs) -> void

  Set water depth.

• depth() const -> T

  Get water depth.

• ~Velocity_potential_solver()virtual
• Velocity_potential_solver()