Roe classical math formulas

oracq.applications.roe_formulas

Plain side-effect-free Roe math functions; callable classically or compilable by compile_function.

oracq.applications.roe_formulas.pick3(index, first, second, third)

Select one of three values by integer index; returns 0.0 when the index is outside 0..2.

Parameters:

• index – Selection index in 0..2; out of range selects no branch.

• first – Value selected for index 0.

• second – Value selected for index 1.

• third – Value selected for index 2.

Returns:

The selected value; 0.0 when the index is out of range.

Return type:

float

oracq.applications.roe_formulas.conserved_to_primitive(rho, momentum, energy, gamma)

Convert one-dimensional Euler conserved variables to primitive variables.

Parameters:

• rho – Density.

• momentum – Momentum density.

• energy – Total energy density.

• gamma – Ratio of specific heats.

Returns:

(velocity, pressure, enthalpy), with enthalpy defined as total energy plus pressure divided by density.

Return type:

tuple

oracq.applications.roe_formulas.euler_entry(velocity, enthalpy, row, col, gamma)

Return the requested element of the one-dimensional Euler flux Jacobian matrix.

Elements are expressed using only flow velocity and enthalpy; row and column indices follow the ordering of the conserved variables (rho, momentum, energy), numbered from zero.

Parameters:

• velocity – Flow velocity.

• enthalpy – Specific enthalpy, defined as in the return value of conserved_to_primitive.

• row – Row index, in 0..2.

• col – Column index, in 0..2.

• gamma – Ratio of specific heats.

Returns:

The element at row row and column col of the Jacobian matrix.

Return type:

float

oracq.applications.roe_formulas.entropy_absolute(eigenvalue, delta)

Absolute value of an eigenvalue with the Harten entropy fix.

When delta is positive and the absolute value of the eigenvalue is smaller, the smoothed value (eigenvalue**2+delta**2)/(2*delta) is returned; otherwise the plain absolute value is returned.

Parameters:

• eigenvalue – The eigenvalue.

• delta – Entropy fix threshold; the fix is disabled when non-positive.

Returns:

The entropy-fixed absolute value of the eigenvalue.

Return type:

float

oracq.applications.roe_formulas.frozen_roe_face(rho_l, m_l, e_l, rho_r, m_r, e_r, row, col, gamma=1.4, entropy_delta=0.125)

Compute the element at the given row and column of the frozen-Roe left and right coefficient matrices.

Roe averaging of the left and right conserved states yields the mean flow velocity and enthalpy; the eigenvalues u-c, u and u+c are made absolute with the entropy fix, and the elements of |A| are assembled as R*diag(a)*R**-1. Combined with the flux Jacobian elements on both sides given by euler_entry, this returns the values of 0.5*(A_l+|A|) and 0.5*(A_r-|A|) at row and col, as the Roe flux share coefficients applied to the left and right states.

Parameters:

• rho_l – Left-side density.

• m_l – Left-side momentum density.

• e_l – Left-side total energy density.

• rho_r – Right-side density.

• m_r – Right-side momentum density.

• e_r – Right-side total energy density.

• row – Row index of the matrix element, in 0..2.

• col – Column index of the matrix element, in 0..2.

• gamma – Ratio of specific heats.

• entropy_delta – Harten entropy fix threshold.

Returns:

(left, right), the elements of the left and right coefficient matrices at the given row and column.

Return type:

tuple