Theory and Modern Applications
From: A mass-conservative higher-order ADI method for solving unsteady convection–diffusion equations
Method | Average error | \(L^{2}\) norm error | \(L^{\infty }\) norm error | |
---|---|---|---|---|
Pe = 100 | ||||
t = 0.01 | DHOC-ADI | 8.05924 × 10−5 | 2.75150 × 10−4 | 2.32611 × 10−3 |
τ = 2.5 × 10−5 | HOC-ADI | 1.25123 × 10−3 | 4.37851 × 10−3 | 4.70167 × 10−2 |
EHOC-ADI | 2.01865 × 10−4 | 7.43597 × 10−4 | 8.83915 × 10−3 | |
RHOC-ADI | 9.64574 × 10−5 | 3.54495 × 10−4 | 3.20386 × 10−3 | |
Pe = 1000 | ||||
t = 0.001 | DHOC-ADI | 8.06267 × 10−5 | 2.79187 × 10−4 | 2.32880 × 10−3 |
τ = 2.5 × 10−6 | HOC-ADI | 1.45299 × 10−3 | 5.31763 × 10−3 | 4.90389 × 10−2 |
EHOC-ADI | 2.16272 × 10−4 | 8.09967 × 10−4 | 9.79204 × 10−3 | |
RHOC-ADI | 1.01878 × 10−4 | 3.81345 × 10−4 | 3.51572 × 10−3 | |
Pe = 10,000 | ||||
t = 0.0001 | DHOC-ADI | 8.09330 × 10−5 | 2.80772 × 10−4 | 2.33917 × 10−3 |
τ = 2.5 × 10−7 | HOC-ADI | 1.46509 × 10−3 | 5.38039 × 10−3 | 4.89280 × 10−2 |
EHOC-ADI | 2.17773 × 10−4 | 8.16985 × 10−4 | 9.89365 × 10−3 | |
RHOC-ADI | 1.02455 × 10−4 | 3.84194 × 10−4 | 3.54963 × 10−3 |