The pressure correction method

Some recent advances in finite volume approach and their applications in the study of heat transfer enhancement

“…However, they do affect the convergence rate. Therefore, since the proposal of the SIM-PLE algorithm, a number of its variants were proposed in order to overcome one or both of the approximations [23][24][25][26][27][28][29][30][31][32][33][34][35]. The SIMPLER algorithm [23] successfully overcomes the first approximation, and is widely used in the current CFD/NHT community.…”

“…Even though there are more than ten variants of the SIMPLE-like algorithm, the second approximation, i.e., the dropping of the neighboring grid effects, have not been successfully resolved so far. These variants include SIMPLEC and SIMPLEX by van Doormaal and Raithby in 1984 and 1985 [24][25][26], PISO by Issa in 1985 [27] and the revised versions by Connell and Stow in 1986 [28], Chatwani and Turan in 1991 [29], Lee and Tzong in 1992 [30], Yen and Liu in 1993 [31], Wen and Ingham [32] in 1993, SIMPLESSEC, SIMPLESSE by Gjesdal and Lossius [33] STOIC (second and third order interpolation for convection)φ [14] HOAB (high-order-accurate bounded scheme)φ [35]. All these variants are usually called SIMPLE-like or SIMPLE-family algorithm.…”

Ellipticity, accuracy, and convergence of the discrete Navier-Stokes equations

“…Several methods have been suggested to recover the full ellipticity of the discrete system and prevent the occurrence of this oscillation [1][2][3][4][5]. In Armfield [ 1 ] a finite volume method was presented that was specifically designed to have an identical discrete ellipticity to the finite volume SIMPLE scheme defined on a staggered mesh [6][7][8][9], which in turn has an identical discrete ellipticity to the standard second-order central differencing for the Laplace operator. The Armfield scheme, which is briefly described in the next section, was obtained by adding additional terms into the continuity equation to recover the ellipticity, while retaining the iterative SIMPLE Poisson pressure correction equation approach.…”

The interaction of thermocapillary convection and low-frequency vibration in nearly-inviscid liquid bridges

“…The pressure-velocity formulation is considered and the discretization is made using the finite volume method of Patankar [28]. The Pressure Correction Method, see Connell and Stow [29], is used to solve the discretized equations obtained from the governing equations. In particular, the SIMPLEC approximation of Van Doormal and Raithby [30] is used.…”