A direct Primitive Variable Recovery Scheme for hyperbolic conservative equations: The case of relativistic...

Area of Science:

• Computational Physics
• Numerical Analysis
• Fluid Dynamics

Background:

• Solving coupled differential conservative equations is crucial in many scientific fields.
• Existing numerical methods often involve complex algebraic systems for primitive variable recovery.
• Ensuring conservation laws and jump conditions is vital for accurate simulations.

Purpose of the Study:

• To develop a novel numerical scheme, the Primitive Variable Recovery Scheme (PVRS).
• To directly compute primitive variables from conservative equations, simplifying calculations.
• To generalize standard techniques for solving coupled differential conservative systems.

Main Methods:

• Applying the chain rule to the time term of conservative equations to derive primitive variables.
• Utilizing a traditional finite volume method for flux calculations to maintain physical constraints.
• Employing a forward finite difference scheme for time evolution.
• Avoiding the solution of algebraic systems for primitive vector recovery.

Main Results:

• The PVRS successfully solves systems of coupled differential conservative equations.
• Demonstrated convergence for special relativistic hydrodynamics shock-tube problems.
• Graphical error visualization confirmed the method's accuracy against analytic solutions.
• The scheme avoids arduous computations associated with traditional methods.

Conclusions:

• The PVRS offers a generalized and efficient approach to solving coupled differential conservative equations.
• This method simplifies numerical hydrodynamics, particularly in special relativistic regimes.
• PVRS enhances computational tractability while preserving essential physical principles.