Basic 2D flow solver using Matlab developed as an assignment from the course Numerics and Flow Simulation offered by Prof. Dr. Andreas Kempf of the University Duisburg-Essen
Link: https://www.uni-due.de/ivg/fluiddynamik/en/index_en.php

• The CDS Scheme is second order accurate but unstable with explicit Euler Time-Integration
• This scheme exhibits strong oscillations as seen below

• A non-standard "educational" scheme that works with reasonable accuracy for explicit Euler Time-Integration (Kempf)
• Point where fluxees are discretised is shifted upstream (assumes constant velocity!)
• USCDS CANNOT consider changes in velocity field or diffusive fluxes

• The UDS Scheme uses the upstream value
• The UDS Scheme is only first order accurate, very dissipative but very stable

• TVD Schemes blend CDS and UDS to remain accurate and avoid wiggles
• Example here, uses the SMART Scheme