An effective method for determining laminar-turbulent unsteady viscous fluid flow in regions with complex shapes is presented.To solve two- and three-dimensional problems for the Navier-Stokes equations written in primitive variables, a modified artificial compressibility method on Cartesian grids was applied. Two numerical approaches were proposed – based on the use of the method of lines in combination with the transfer of all variables from the boundaries of the regions to the nearest nodes of uniform computational grids. The results of test numerical calculations for four cavities with one moving wall are presented: square, semicircular, half-cubic, and hemispherical – compared with numerical simulations performed using the Fluent program.
SOLUTIONS OF UNSTEADY INCOMPRESSIBLE NAVIERSTOKES EQUATIONS FOR TWO- AND THREE-DIMENSIONAL SHEAR DRIVEN CAVITY FLOWS
An efficient method for simulating unsteady laminar-turbulent flows in complex geometries is presented. The extension of the artificial compressibility method to unsteady flows was applied to solve two- and three-dimensional Navier-Stokes equations in primitive variables on Cartesian grids. Two numerical approaches were proposed in this work, which are based on the method of lines process in conjunction with transfer of all the variables from the boundaries to the nearest uniform grid knots. Some test numerical calculations for flows in half-square, semicircular, half-cubic and hemisphere cavities with one uniform moving wall were reported. The present results were compared with the Fluent solver numerical simulations. (…)
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Source: Logistyka Magazine