A Novel Algorithm of Advection Procedure in Volume of Fluid Method to Model Free Surface Flows

Table 2

Velocity calculation for new arrangement in MYV method.

Velocity component	Case	Velocity formula
𝑈𝐶𝐺	A	𝑈(𝐼,𝐽)+𝑆^𝑏3(𝑈(𝐼−1,𝐽)−𝑈(𝐼,𝐽))
	B	𝑈(𝐼,𝐽)+𝑆^𝑟+2𝑆𝑙3(𝑆𝑟+𝑆𝑙)(𝑈(𝐼−1,𝐽)−𝑈(𝐼,𝐽))
	C	𝑈(𝐼−1,𝐽)+1−4𝑆^2𝑡+4𝑆^2𝑏−5𝑆𝑡𝑆𝑏3(𝑆𝑡+𝑆𝑏)(𝑈(𝐼,𝐽)−𝑈(𝐼−1,𝐽))
	D	𝑈(𝐼,𝐽)+1−3−(1−𝑆^𝑡)^2(1−𝑆𝑙)6−3(1−𝑆𝑡)(1−𝑆𝑙)(𝑈(𝐼−1,𝐽)−𝑈(𝐼,𝐽))
𝑉𝐶𝐺	A	𝑉(𝐼,𝐽)+1−𝑆^𝑙3(𝑉(𝐼,𝐽−1)−𝑉(𝐼,𝐽))
	B	𝑉(𝐼,𝐽)+1−4𝑆^2𝑙+4𝑆^2𝑟−5𝑆𝑟𝑆𝑙3(𝑆𝑙+𝑆𝑟)(𝑉(𝐼,𝐽−1)−𝑉(𝐼,𝐽))
	C	𝑉(𝐼,𝐽)+𝑆^𝑡+2𝑆𝑏3(𝑆𝑡+𝑆𝑏)(𝑉(𝐼,𝐽−1)−𝑉(𝐼,𝐽))
	D	𝑉(𝐼,𝐽)+1−3−(1−𝑆^𝑡)(1−𝑆𝑙)(2+𝑆𝑙)6−3(1−𝑆𝑡)(1−𝑆𝑙)(𝑉(𝐼,𝐽−1)−𝑉(𝐼,𝐽))