Solution on simple Riemann problems (Greenshields flow)
Prediction of different schemes on Riemann problems with different flows
Expansion wave
Shock wave
Prediction of schemes on piecewise-constant initial conditions with different flows
Note: Each row is a different initial condition. The five different initial conditions are kept the same across all plots. On a given row, the leftmost column is the true solution, and all following columns try to approximate it through various numerical methods.
Flow: Greenshields
Flow: Triangular (Symmetrical)
Flow: Triangular (Skewed)
Flow: Trapezoidal
Flow: Greenberg
Flow: Underwood
Movies
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Prediction of a rarefaction wave
Prediction of a shock wave
Solutions for six variants of LWR on the same initial condition
Predictions on Greenshields LWR
Predictions on Triangular LWR (Symmetric)
Predictions on Triangular LWR (Skewed)
Predictions on Trapezoidal LWR
Predictions on Greenberg LWR
Predictions on Underwood LWR
NFV 5x5 outperforms Godunov at predicting a solution of the LWR equation with triangular flow
NFV 5x5 outperforms Godunov at predicting a solution of Burger's equation
Accuracy of NFV 5x5 against the ground truth solution
