Table 3.
Overview of the multiple time-stepping algorithms for the multiscale model
| ▶ | vp ← vp + λp · (Δt/m) · FP | DPD |
| ▶ | For l1 = 0 … K1 − 1 | DPD-CGMD |
| ▶ | set δt1 ≡ Δt/K1 | DPD-CGMD |
| ▶ | vm ← vm + λm · (δt1/m) · FM | DPD-CGMD |
| ▶ | For l2 = 0 … K2 − 1 | CGMD-NB |
| ▶ | set δt2 ≡ δt1/K2 = Δt/(K1 · K2) | CGMD-NB |
| ▶ | vn ← vn + (δt2/2m) · FN | CGMD-NB |
| ▶ | For l3 = 0 … K3 − 1 | CGMD-BD |
| ▶ | set δt ≡ δt3 = δt2/K3 = Δt/(K1 · K2 · K3) | CGMD-BD |
| ▶ | vb ← vb + (δt/2m) · FB | CGMD-BD |
| ▶ | r ← r + δt · v | All Particles |
| ▶ | Communication of positions and velocities. | |
| ▶ | compute FB(r) | CGMD-BD |
| ▶ | Communication of forces. | |
| ▶ | vb ← vb + (δt/2m) · FB | CGMD-BD |
| ▶ | compute FN(r) | CGMD-NB |
| ▶ | Communication of forces. | |
| ▶ | vn ← vn + (δt2/2m) · FN | CGMD-NB |
| ▶ | compute F̃M(r, v) | DPD-CGMD |
| ▶ | Communication of forces. | |
| ▶ | vm ← vm + (δt1/2m) · (FM + F̃M) | DPD-CGMD |
| ▶ | FM ← F̃M | DPD-CGMD |
| ▶ | compute F̃P(r, v) | DPD |
| ▶ | Communication of forces. | |
| ▶ | Add external forces to the viscous flow if any. | Add Forces to flow |
| ▶ | vp ← vp + (Δt/2m) · (FP + F̃P) | DPD |
| ▶ | FP ← F̃P | DPD |