Semi-Implicit Method for Pressure-Linked

The pneumatic drying model was solved numerically for the drying processes of sand particles. The numerical procedure includes discretization of the calculation domain into torus-shaped final volumes, and solving the model equations by implementation of the semi-implicit method for pressure-linked equations (SIMPLE) algorithm [16]. The numerical procedure also implemented the Interphase Slip Algorithm (IPSA) of [17] in order to account the various coupling between the phases. The simulation stopped when the moisture content of a particle falls to a predefined value or when the flow reaches the exit of the pneumatic dryer. 

One of the popular methods proposed by Patankar and Spalding (1972) is called SIMPLE (semi-implicit method for pressure linked equations). In this method, discretized momentum equations are solved using the guessed pressure field. The discretized form of the momentum equations can be written ... 

SIMPLE Semi-implicit method for pressure linked equations... 

Once the pressure correction has been solved for, the velocities are updated using (12.165) and (12.166). This procedure is known as the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm [140, 141]. 

SIMPLE Semi-Implicit Method for Pressure-Linked Equations... 

Several algorithms do exist in the literature for numerical computation of fluid flow problems on the basis of primitive variables, in a finite volume framework. One of the most commonly used algorithms of this kind is the SIMPLE (semi-implicit method for pressure-linked equations) algorithm [2]. With reference to a generic staggered control volume for solution of the momentum equation for u (see Fig. 3) and with similar considerations for Ihe other velocity components, major steps of the SIMPLE algorithm can be summarized as follows ... 

The solution strategy is somewhat varied by the last step since the approach used to linearize and solve the discretized equations varies with the solver type. The two commonly employed solvers in the FVM 2se pressure-based and density-based solvers [ 12,16]. In both methods the velocity field is obtained from the momentum equations. In the density-based approach, the continuity equation is used to obtain the density field, while the pressure field is determined from an equation of state. On the other hand, the pressure-based solver extracts the pressure field by solving the pressure or pressure correction equation, which is obtained by manipulation of the momentum and continuity equations [16]. Implementation of the pressure-based solver via the so-called Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm [12] is explained later. Details of the density-based solver are extensively covered elsewhere [16] and will not be discussed here. 

The semi-implicit method for pressure-linked equations (SIMPLE) algorithm [73] is used for the computation of pressure and velocity vectors of the fluid in each cell. 

SIMPLE Algorithm. For 3D simulations, the three equations of motion [eq. (5-6)] and the equation of continuity [eq. (5-5)] combine to form four equations for four unknowns the pressure and the three velocity components. Because there is no explicit equation for the pressure, special techniques have been devised to extract it in an alternative manner. The best known of these techniques is the SIMPLE algorithm, semi-implicit method for pressure-linked equations (Patankar, 1980). Indeed, a family of algorithms has been derived from this basic one, each of which has a small modification that makes it well suited to one application or another. 

Simple High-Accuracy Resolution Program Semi-Implicit Method for Pressure-Linked Equations SIMPLE Consistent Simple Line Interface Calculation Spectral Method... 

This solution algorithm for calculating the flow fields has been given the name SIMPLE. The acronym SIMPLE stands for Seml-ImpUcit Method for Pressure-Linked Equations. The words semi-implicit in the name SIMPLE have been used to acknowledge the omission of the neighboring terms nb inb >... 

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