Solution of the 1D Special Relativistic Hydrodynamics(SRH) Equations Using Different Numerical Method and Results from Different Test Problems

TL;DR

This paper compares different numerical methods for solving 1D special relativistic hydrodynamics equations, highlighting the strengths and limitations of Non-TVD and TVD schemes in handling smooth and discontinuous wave problems.

Contribution

It provides a comparative analysis of Non-TVD and TVD numerical schemes applied to 1D SRH equations, demonstrating their respective advantages and drawbacks.

Findings

Non-TVD schemes yield better solutions for smooth waves.

TVD schemes effectively eliminate oscillations at discontinuities.

TVD schemes may reduce local accuracy near extrema.

Abstract

In this paper, we have solved 1D special relativistic hydrodynamical equations using different numerical method in computational gas dynamics. The numerical solutions of these equations for smooth wave cases give better solution when we use $Non-TVD$(Total Variable Diminishing) but solution of discontinuity wave produces some oscillation behind the shock. On the other hand, $TVD$ type schemes give good approximation at discontinuity cases. Because $TVD$ schemes completely remove the oscillations, they reduce locally the accuracy of the solution around the extrema.