![Sample our Engineering & Technology journals, sign in here to start your access, latest two full volumes FREE to you for 14 days]({"type":"image" , "src" : "/sda/5933/TOC-Subject-Sample-2021-Engineering-Tech.jpg"})
ABSTRACT
This paper proposes an efficient segregated solution procedure for the two-dimensional incompressible fluid flow on unstructured grids. The new algorithm is called SIMPLERR (SIMPLERR-revised algorithm). It includes an inner iterative process that consists of a pressure equation solution and an explicit velocity correction, and then, the pressure field is obtained by another solving process for the pressure equation. The features and advantages of the SIMPLERR algorithm are demonstrated by solving a benchmark flow problem, and the results indicate that the SIMPLERR algorithm can maintain a strong stability as the IDEAL algorithm and can converge faster than the SIMPLER algorithm or even than the IDEAL algorithm. The advantage of the SIMPLERR algorithm is especially evident for high-Re and fine-mesh fluid flow cases, where the SIMPLERR algorithm and the IDEAL algorithm can obtain a convergence result but the SIMPLER algorithm cannot. The SIMPLERR algorithm is about two times faster than the IDEAL algorithm.
Nomenclature
| A | = | face area vector (or coefficient matrix) |
| A | = | face area |
| b | = | source term for a scalar equation |
| B | = | source term vector for a linear system |
| ds | = | distance from P to NB |
| d | = | unit vector along a connecting line |
| D | = | vector along a connecting line |
| m | = | mass flux |
| M | = | midpoint of interface |
| n | = | unit vector normal to face |
| p | = | isotropic pressure |
| P, NB | = | cell centroid |
| r | = | Sweby’s r-factor |
| r | = | position vector |
| R | = | residual |
| Re | = | Reynolds number |
| S | = | source term |
| t | = | time |
| t | = | unit vector tangential to a face |
| T | = | tangential vector to a face |
| U | = | upwind point |
| V | = | vector of velocity |
| α | = | scaling factor (or relaxation factor) |
| γ | = | scaling factor |
| Γ | = | diffusion coefficient |
| ρ | = | fluid density |
| ϕ | = | dependent variable |
| Ω | = | integral volume |
| ψ | = | Sweby’s flux limiter |
| Subscripts | = | |
| bd | = | boundary face designator |
| f | = | face |
| NB | = | neighboring cell designator |
| P | = | main cell designator |
| Superscripts | = | |
| FO | = | first-order scheme |
| HO | = | higher-order scheme |
| * | = | previous iteration |
| # | = | intermediate value |
Nomenclature
| A | = | face area vector (or coefficient matrix) |
| A | = | face area |
| b | = | source term for a scalar equation |
| B | = | source term vector for a linear system |
| ds | = | distance from P to NB |
| d | = | unit vector along a connecting line |
| D | = | vector along a connecting line |
| m | = | mass flux |
| M | = | midpoint of interface |
| n | = | unit vector normal to face |
| p | = | isotropic pressure |
| P, NB | = | cell centroid |
| r | = | Sweby’s r-factor |
| r | = | position vector |
| R | = | residual |
| Re | = | Reynolds number |
| S | = | source term |
| t | = | time |
| t | = | unit vector tangential to a face |
| T | = | tangential vector to a face |
| U | = | upwind point |
| V | = | vector of velocity |
| α | = | scaling factor (or relaxation factor) |
| γ | = | scaling factor |
| Γ | = | diffusion coefficient |
| ρ | = | fluid density |
| ϕ | = | dependent variable |
| Ω | = | integral volume |
| ψ | = | Sweby’s flux limiter |
| Subscripts | = | |
| bd | = | boundary face designator |
| f | = | face |
| NB | = | neighboring cell designator |
| P | = | main cell designator |
| Superscripts | = | |
| FO | = | first-order scheme |
| HO | = | higher-order scheme |
| * | = | previous iteration |
| # | = | intermediate value |