CFDLab Toolkit: 1D Riemann Problem Exact Solver (GUI)

A 1D Exact Riemann Solver (GUI), designed as a benchmark for validating CFD schemes.

This MATLAB App is a component of the CFDLab Toolkit. It provides an interactive Graphical User Interface (GUI) for computing the exact solution to the one-dimensional Riemann problem for the time-dependent Euler equations of gas dynamics.

The exact solution to the 1D Riemann problem serves as a definitive benchmark for evaluating the performance of CFD numerical schemes, such as TVD and WENO schemes. While researchers often employ numerical solutions computed on extremely fine meshes as "reference solutions," these approximations cannot entirely eliminate numerical dissipation and dispersion. In contrast, the exact solver, based on analytical derivation, guarantees the capture of discontinuities with absolute sharpness.

A standout feature of this program is its efficient two-stage workflow. Following a single pre-computation of the initial wave structure, it generates reusable function handles. This enables users to rapidly obtain the exact solution at any arbitrary spatiotemporal point (x, t) without the need to re-solve the Riemann problem.

First Run Demo:

Vacuum Robustness & Small Time Demo: