Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Relative errors-Mesh size =h= 0_34 × 10−3_
| M(t = 1) | W(t = 1) | M(t = 3) | W(t = 3) | M(t = 5) | W(t = 5) | |
|---|---|---|---|---|---|---|
| Relative L2-error | 1.82 × 10−6 | 1.48 × 10−7 | 9.70 × 10−8 | 1.39 × 10−7 | 6.09 × 10−8 | 1.36 × 10−7 |
| Relative L∞-error | 1.35 × 10−3 | 3.85 × 10−4 | 3.11 × 10−4 | 3.72 × 10−4 | 2.47 × 10−4 | 3.69 × 10−4 |
Model variables and parameters associated with System (3)_
| Variables | Description |
|---|---|
| M, W | The density of species 1 and 2 |
| C | The concentration of the chemical |
| U, P | The velocity and the pressure of the fluid |
| Q, R and S | The anisotropic diffusive tensors |
| a(M), b(W) | The density-dependent diffusion coefficients |
| χ1(M), χ2(W) | The chemotactic sensitivity functions |
| μ1, μ2 > 0 | The growth rate of populations 1 and 2 |
| α1, α2 > 0 | The strength of populations 1 and 2 in competition |
| α, β > 0 | The consumption rate of chemicals by populations 1 and 2 |
| The external gravitational force exerted by the species 1 and 2 on the fluid |
Relative errors-Mesh size =h= 0_54 × 10−2_
| M(t = 1) | W(t = 1) | M(t = 3) | W(t = 3) | M(t = 5) | W(t = 5) | |
|---|---|---|---|---|---|---|
| Relative L2-error | 3.09 × 10−6 | 3.36 × 10−7 | 1.21 × 10−7 | 1.16 × 10−7 | 6.43 × 10−8 | 6.80 × 10−8 |
| Relative L∞-error | 1.76 × 10−3 | 5.80 × 10−4 | 3.48 × 10−4 | 3.41 × 10−4 | 2.54 × 10−4 | 2.61 × 10−4 |