The use of conjugate gradients methods with a segregated finite volume procedure for solving transient, incompressible Navier-Stokes equations

• Published in: Communications in numerical methods in engineering Vol. 11; no. 10; pp. 849 - 856
• Main Authors: Nieplocha, J., Schreiber, W. C.
• Format: Journal Article
• Language: English
• Published: Sussex John Wiley & Sons, Ltd 01.10.1995; Wiley
• Subjects: Computational methods in fluid dynamics; conjugate gradient methods; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); incompressible Navier-Stokes equations; Physics; segregated finite volume procedure; staggered grid; vectorization; Conjugate gradient method; Transient flow; Finite volume method; Numerical method; Supercomputers; Incompressible fluid; Jacobi matrix; Viscous fluids; Preconditioning; Vectorization; Navier-Stokes equations
• ISSN: 1069-8299; 1099-0887
• DOI: 10.1002/cnm.1640111009

PISO (pressure‐implicit with splitting of operators) is an algorithm devised to solve the transient incompressible Navier–Stokes and energy equations. In that it uses separate equations for each of two pressure corrections, velocity components and transported scalars, PISO is known as a segregated solution procedure. Preconditioned, generalized conjugate gradient (GCG) methods in combination with schemes for vectorization and storage minimization are described in the paper for the purpose of solving both the symmetric and non‐symmetric algebraic equation systems that result from the PISO algorithm. Of particular interest in the paper is a comparison of the present procedure with a procedure described by Chin et al. (1992) in which preconditioned conjugate gradient methods are used to solve the Jacobian matrix used in the Newton iteration of the fully coupled non‐linear equations. The two methods are similar in that both techniques are based on a discretization using staggered control volumes with the power‐law method for modelling advection‐diffusion transport.