Study on the Convective Term Discretized by Strong Conservation and Weak Conservation Schemes for Incompressible Fluid Flow and Heat Transfer

Table 1

Discretized expressions of the convective flux at the interface (𝜌𝐴𝑢𝜙)_𝑒.

Discrete format	Weak; conservation scheme	Strong; conservation scheme	Condition
FUD	𝜌𝑒𝐴𝑒𝑢𝑒𝜙𝑃	𝜌𝐴𝑢𝜙𝑃	𝑢𝑒≥0
	𝜌𝑒𝐴𝑒𝑢𝑒𝜙𝐸	𝜌𝐴𝑢𝜙𝐸	𝑢𝑒<0
SUD	𝜌𝑒𝐴𝑒𝑢𝑒3𝜙𝑃−𝜙𝑊2	3𝜌𝐴𝑢𝜙𝑃−𝜌𝐴𝑢𝜙𝑊2	𝑢𝑒≥0
	𝜌𝑒𝐴𝑒𝑢𝑒3𝜙𝐸−𝜙𝐸𝐸2	3𝜌𝐴𝑢𝜙𝐸−𝜌𝐴𝑢𝜙𝐸𝐸2	𝑢𝑒<0
CD	𝜌𝑒𝐴𝑒𝑢𝑒𝜙𝑃+𝜙𝐸2	𝜌𝐴𝑢𝜙𝑃+𝜌𝐴𝑢𝜙𝐸2	—
QUICK	𝜌𝑒𝐴𝑒𝑢𝑒3𝜙𝐸+6𝜙𝑃−𝜙𝑊8	3𝜌𝐴𝑢𝜙𝐸+6𝜌𝐴𝑢𝜙𝑃−𝜌𝐴𝑢𝜙𝑊8	𝑢𝑒≥0
	𝜌𝑒𝐴𝑒𝑢𝑒3𝜙𝑃+6𝜙𝐸−𝜙𝐸𝐸8	3𝜌𝐴𝑢𝜙𝑃+6𝜌𝐴𝑢𝜙𝐸−𝜌𝐴𝑢𝜙𝐸𝐸8	𝑢𝑒<0