# The SIMPLE Algorithm

(Difference between revisions)
 Revision as of 04:41, 7 April 2010 (view source) (Created page with 'The above approach for the solution of the incompressible flow field was named SIMPLE, which stands for Semi-Implicit Method for Pressure-Linked Equations. It was originally prop…')← Older edit Current revision as of 16:17, 2 June 2010 (view source) (2 intermediate revisions not shown) Line 1: Line 1: - The above approach for the solution of the incompressible flow field was named SIMPLE, which stands for Semi-Implicit Method for Pressure-Linked Equations. It was originally proposed by Patankar and Spalding (1972) and summarized in Patankar (1980). This algorithm is a semi-implicit method because the first terms on the right-hand side of eqs. (4.300) – (4.302) are neglected. If these terms are retained, we will have to solve for the velocity corrections ( ) for the entire flow field simultaneously and the algorithm will become fully-implicit. The procedure for SIMPLE algorithm can be summarized as following: + {{Comp Method for Forced Convection Category}} - 1. Guess a pressure field, p*. + The above approach for the solution of the incompressible flow field was named SIMPLE, which stands for Semi-Implicit Method for Pressure-Linked Equations. It was originally proposed by Patankar and Spalding (1972) and summarized in Patankar (1980). This algorithm is a semi-implicit method because the first terms on the right-hand side of eqs. (4.300) – (4.302) are neglected. If these terms are retained, we will have to solve for the velocity corrections ( ) for the entire flow field simultaneously and the algorithm will become fully-implicit. The procedure for SIMPLE algorithm can be summarized as following:
- 2. Obtain the starred velocity field, (u*, v*, and w*) from eqs. (4.295) – (4.297). + 1. Guess a pressure field, p*.
- 3. Solve the pressure correction equation (4.309) to get  . + 2. Obtain the starred velocity field, (u*, v*, and w*) from eqs. (4.295) – (4.297).
- 4. Obtain a new pressure field from eq. (4.298). + 3. Solve the pressure correction equation (4.309) to get  .
- 5. Improve the velocity field using eqs. (4.305) – (4.307). + 4. Obtain a new pressure field from eq. (4.298).
- 6. Obtain solutions for other  ’s from eq. (4.274). If the flow field is not affected by a particular  , it should be solved after a converged solution for flow field is obtained. + 5. Improve the velocity field using eqs. (4.305) – (4.307).
- 7. Treat the corrected pressure in Step 4 as a new starred pressure and go back to step 2. The iteration procedure is repeated until a converged solution is obtained. + 6. Obtain solutions for other  ’s from eq. (4.274). If the flow field is not affected by a particular  , it should be solved after a converged solution for flow field is obtained.
+ 7. Treat the corrected pressure in Step 4 as a new starred pressure and go back to step 2. The iteration procedure is repeated until a converged solution is obtained.
Since the invention of the SIMPLE algorithm in 1972, it has evolved into the classic approach for computational fluid dynamics and heat transfer. Although there are several improved versions in the literature, SIMPLE still remains one of basic the most powerful algorithms. The objective of this section is to introduce the readers to the world of computational fluid dynamics and heat transfer without the overwhelming numerical details. Additional information can be found in the seminal books of Patankar (1980) and Tao (2001), as well as the Handbook of Numerical Heat Transfer (Minkowycz et al., 2006). Since the invention of the SIMPLE algorithm in 1972, it has evolved into the classic approach for computational fluid dynamics and heat transfer. Although there are several improved versions in the literature, SIMPLE still remains one of basic the most powerful algorithms. The objective of this section is to introduce the readers to the world of computational fluid dynamics and heat transfer without the overwhelming numerical details. Additional information can be found in the seminal books of Patankar (1980) and Tao (2001), as well as the Handbook of Numerical Heat Transfer (Minkowycz et al., 2006).

## Current revision as of 16:17, 2 June 2010

The above approach for the solution of the incompressible flow field was named SIMPLE, which stands for Semi-Implicit Method for Pressure-Linked Equations. It was originally proposed by Patankar and Spalding (1972) and summarized in Patankar (1980). This algorithm is a semi-implicit method because the first terms on the right-hand side of eqs. (4.300) – (4.302) are neglected. If these terms are retained, we will have to solve for the velocity corrections ( ) for the entire flow field simultaneously and the algorithm will become fully-implicit. The procedure for SIMPLE algorithm can be summarized as following:
1. Guess a pressure field, p*.
2. Obtain the starred velocity field, (u*, v*, and w*) from eqs. (4.295) – (4.297).
3. Solve the pressure correction equation (4.309) to get .
4. Obtain a new pressure field from eq. (4.298).
5. Improve the velocity field using eqs. (4.305) – (4.307).
6. Obtain solutions for other ’s from eq. (4.274). If the flow field is not affected by a particular , it should be solved after a converged solution for flow field is obtained.
7. Treat the corrected pressure in Step 4 as a new starred pressure and go back to step 2. The iteration procedure is repeated until a converged solution is obtained.
Since the invention of the SIMPLE algorithm in 1972, it has evolved into the classic approach for computational fluid dynamics and heat transfer. Although there are several improved versions in the literature, SIMPLE still remains one of basic the most powerful algorithms. The objective of this section is to introduce the readers to the world of computational fluid dynamics and heat transfer without the overwhelming numerical details. Additional information can be found in the seminal books of Patankar (1980) and Tao (2001), as well as the Handbook of Numerical Heat Transfer (Minkowycz et al., 2006).