A method for computing three dimensional flows using non‐orthogonal boundary‐fitted co‐ordinates

Abstract

SUMMARYFor three-dimensional fluid flows in complex geometries, it is convenient to make predictions using a non-orthogonal boundary-fitted mesh. The present paper describes an economical method of solving the equations of motion for two and three dimensional problems using such meshes. The locations on the mesh at which the depenent variables are calculated, and the methods used to solve the equations, are key issues in the development of a successful algorithm; these are discussed in the present paper. Results obtained when the proposed method is applied to several problems are also described. The method is intended for flows in which compressibility effects do not dominate.

A numerical method for solving the 3D unsteady incompressible Navier–Stokes equations in curvilinear domains with complex immersed boundaries

“…(16) reads as follows: (18) where is the same discrete curvilinear pressure gradient operator defined as in Eq. (15). Obviously the proposed method is substantially more efficient that the FT-2 approach as it does not require the discretization of the convective and viscous terms for all three momentum equations at each surface center-a step, which as discussed earlier essentially triples the amount of computational work compared to a non-staggered grid method.…”

“…This approach has been successfully applied in the past, see for example Maliska and Raithby [15], but it essentially triples the computational cost of the curvilinear formulation relative to the Cartesian formulation as in the latter only one momentum equation is solved at each surface center. This increased cost could be very expensive in 3D simulations and has prompted the development of approximate formulations, which de-fine only one Cartesian component at each surface center of the curvilinear staggered mesh (i.e., u 1 component at all (i + 1/2, j,k) locations and u 2 , u 3 for the other two surface centers, respectively) and reconstruct the other two by interpolation-this approach will be denoted as PT-2.…”

“…(13). At the (i + 1/2, j, k) nodes, for instance, the V 1 equation is semidiscretized as follows: (14) where (15) is the pressure gradient operator for curvilinear cooordinates and δ ξr is the central differencing operator at the surface center. The advantage of using the above discretization approach over the FT-1 formulation is that the explicit evaluation of the Christoffel symbols is avoided.…”

Numerical model for the prediction of dilute, three‐dimensional, turbulent fluid–particle flows, using a Lagrangian approach for particle tracking and a CVFEM for the carrier phase

“…The need to handle irregular geometries has become a requirement today as a consequence of the increasing use of CFD for the solution of real problems, especially in industry. Numerical methods based on structured boundary-fitted orthogonal or non-orthogonal grids are frequently adopted for predicting flows in irregular geometries, with good results [6][7][8][9]. However, methods based on finite element meshes have become the methods of choice for the prediction of flows in complex geometries [10][11][12]).…”

Optimization of the Interfacial Shear Stress and Assessment of Closure Relations for Horizontal Viscous Oil-Gas Flows in the Stratified and Slug Regimes

“…The systems are solved sequentially in each iteration in which pressure-velocity coupling is handled with the Pressure Implicit Momentum Explicit (PRIME) algorithm (Maliska & Raithby, 1984) modified by Ortega & Nieckele (2005).…”