Classes
class	MachSolverResult

Functions
float	calculate_area_mach_ratio (float M, float gamma)
float	calculate_area_mach_derivative (float M, float gamma, Optional[float] A_Astar=None)
float	estimate_initial_mach (float eps, float gamma, bool supersonic=True)
MachSolverResult	solve_mach_from_area_ratio (float eps, float gamma, bool supersonic=True, float tolerance=1e-10, int max_iterations=50, Optional[float] initial_guess=None)
Tuple[float, bool]	solve_mach_robust (float eps, float gamma, bool supersonic=True)
Tuple[float, bool]	solve_exit_mach_robust (float eps, float gamma)
MachSolverResult	solve_exit_mach_from_area_ratio (float eps, float gamma, **kwargs)

Detailed Description

Mach number solver for isentropic nozzle flow.

This module provides the area-Mach relation solver used throughout the nozzle
calculations. Consolidates previously duplicated Newton-Raphson implementations.

Physics:
    The area-Mach relation for isentropic flow:
    A/A* = (1/M) × [(2/(γ+1)) × (1 + (γ-1)/2 × M²)]^((γ+1)/(2(γ-1)))
    
    For a given area ratio ε = A/A* > 1, there are two solutions:
    1. Subsonic solution (M < 1)
    2. Supersonic solution (M > 1)

Function Documentation

◆ calculate_area_mach_derivative()

float engine.core.mach_solver.calculate_area_mach_derivative	(	float	M,
		float	gamma,
		Optional[float]	A_Astar = None )

Calculate derivative d(A/A*)/dM for Newton-Raphson solver.

Parameters
----------
M : float
    Mach number
gamma : float
    Specific heat ratio
A_Astar : float, optional
    Pre-calculated A/A* (for efficiency)
    
Returns
-------
dA_dM : float
    Derivative of area ratio with respect to Mach number

Definition at line 61 of file mach_solver.py.

References calculate_area_mach_ratio().

Referenced by solve_mach_from_area_ratio().

◆ calculate_area_mach_ratio()

float engine.core.mach_solver.calculate_area_mach_ratio	(	float	M,
		float	gamma )

Calculate area ratio A/A* for given Mach number and gamma.

A/A* = (1/M) × [(2/(γ+1)) × (1 + (γ-1)/2 × M²)]^((γ+1)/(2(γ-1)))

Parameters
----------
M : float
    Mach number (must be > 0)
gamma : float
    Specific heat ratio (must be > 1)
    
Returns
-------
A_Astar : float
    Area ratio A/A*

Definition at line 33 of file mach_solver.py.

Referenced by calculate_area_mach_derivative(), and solve_mach_from_area_ratio().

◆ estimate_initial_mach()

float engine.core.mach_solver.estimate_initial_mach	(	float	eps,
		float	gamma,
		bool	supersonic = True )

Estimate initial Mach number for given area ratio.

Parameters
----------
eps : float
    Area ratio A/A* (must be >= 1)
gamma : float
    Specific heat ratio
supersonic : bool
    Whether to estimate the supersonic solution (M > 1) or subsonic (M < 1)
    
Returns
-------
M_guess : float
    Initial guess for Mach number

Definition at line 90 of file mach_solver.py.

References max.

Referenced by solve_mach_from_area_ratio().

◆ solve_exit_mach_from_area_ratio()

MachSolverResult engine.core.mach_solver.solve_exit_mach_from_area_ratio	(	float	eps,
		float	gamma,
		**	kwargs )

Backward compatible wrapper for supersonic exit Mach solver.

Definition at line 334 of file mach_solver.py.

References solve_mach_from_area_ratio().

◆ solve_exit_mach_robust()

Tuple[float, bool] engine.core.mach_solver.solve_exit_mach_robust	(	float	eps,
		float	gamma )

Backward compatible wrapper for supersonic exit Mach solver.

Definition at line 324 of file mach_solver.py.

References solve_mach_robust().

◆ solve_mach_from_area_ratio()

MachSolverResult engine.core.mach_solver.solve_mach_from_area_ratio	(	float	eps,
		float	gamma,
		bool	supersonic = True,
		float	tolerance = 1e-10,
		int	max_iterations = 50,
		Optional[float]	initial_guess = None )

Solve for Mach number given area ratio using Newton-Raphson.

Finds either the supersonic (M > 1) or subsonic (M < 1) solution.

Parameters
----------
eps : float
    Area ratio A/A* (must be >= 1)
gamma : float
    Specific heat ratio (must be > 1)
supersonic : bool
    Whether to find the supersonic or subsonic solution
tolerance : float
    Convergence tolerance for residual
max_iterations : int
    Maximum Newton-Raphson iterations
initial_guess : float, optional
    Initial guess for M (if None, uses estimate_initial_mach)
    
Returns
-------
result : MachSolverResult
    Solver result with M, convergence info, and diagnostics

Definition at line 151 of file mach_solver.py.

References calculate_area_mach_derivative(), calculate_area_mach_ratio(), and estimate_initial_mach().

Referenced by solve_exit_mach_from_area_ratio(), and solve_mach_robust().

◆ solve_mach_robust()

Tuple[float, bool] engine.core.mach_solver.solve_mach_robust	(	float	eps,
		float	gamma,
		bool	supersonic = True )

Robust wrapper for Mach solver with automatic fallback.

Parameters
----------
eps : float
    Area ratio A/A*
gamma : float
    Specific heat ratio
supersonic : bool
    Whether to find the supersonic or subsonic solution
    
Returns
-------
M : float
    Mach number solution
success : bool
    Whether solver converged successfully

Definition at line 267 of file mach_solver.py.