Struct dzahui::solvers::fem::stokes_solver::dim1::StokesSolver1D

pub struct StokesSolver1D {
    pub(crate) stiffness_matrix: Array2<f64>,
    pub(crate) b_vector: Array1<f64>,
    pub gauss_step: usize,
    pub hydrostatic_pressure: f64,
    pub rho: f64,
}

General Information

A Stokes solver 1d abstracts the equation: “(1/ρ)p_x = f” with constant velocity and hydrostatic pressure “ρ”

Fields

• boundary_condition_pressure - Original boundary conditions (Only Dirichlet is supported for now).
• stiffness_matrix - Left-side matrix of resulting discrete equation.
• b_vector - Right-side vector of the resulting discrete equation.
• gauss_step - Precision of quadrature.
• speed - Constant speed.
• rho - Constant density.

Fields

stiffness_matrix: Array2<f64>

b_vector: Array1<f64>

gauss_step: usize

hydrostatic_pressure: f64

rho: f64

Implementations

impl StokesSolver1D

pub fn new(
    params: &StokesParams1D,
    mesh: Vec<f64>,
    gauss_step: usize
) -> Result<Self, Error>

Creates a new instance of solver from params

pub fn gauss_legendre_integration(
    rho: f64,
    hydrostatic_pressure: f64,
    mesh: &Vec<f64>,
    gauss_step: usize,
    function: &Box<dyn Fn(f64) -> f64>
) -> Result<(Array2<f64>, Array1<f64>), Error>

General Information

First, it generates the basis for a solver from the linear basis constructor. Then the stiffnes matrix and vector b are generated based on linear basis integration via Gauss-Legendre and returned. Note that vector and matrix will have one on their diagonals’ boundaries and zero on other boundary elements to make boundary conditions permanent.

Parameters

• rho - density
• hydrostatic_pressure
• mesh - Vector of f64 representing a line
• gauss_step - How many nodes will be calculated for a given integration
• function - Force acting on the fluid

Returns

A tuple with both the stiffness matrix and the vector b.

Trait Implementations

impl Debug for StokesSolver1D

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl DiffEquationSolver for StokesSolver1D

fn solve(&mut self, _time_step: f64) -> Result<Vec<f64>, Error>

Specific implementation

Solving starts by obtaining stiffness matrix and vector b (Ax=b). Then both are used inside function solve_by_thomas to obtain the result vector.