Abstract
Numerical simulation of fluid flow and heat or mass transfer phenomenon requires numerical solution of Navier–Stokes and energy-conservation equations, together with the continuity equation. The basic problem of solving general transport equations by the Finite Volume Method (FVM) is the exact calculation of the transport quantity. Numerical or false diffusion is a phenomenon of inserting errors in calculations that threaten the accuracy of the computational solution. The paper compares the physical accuracy of the calculation in the Computational Fluid Dynamics (CFD) code in Ansys Fluent using the offered discretization calculation schemes, methods of solving the gradients of the transport quantity on the cell walls, and the influence of the mesh type. The paper offers possibilities on how to reduce numerical errors. In the calculation area, the sharp boundary of two areas with different temperatures is created in the flow direction. The three-dimensional (3D) stationary flow of the fictitious gas is simulated using FVM so that only advective transfer, in terms of momentum and heat, arises. The subject of the study is to determine the level of numerical diffusion (temperature field scattering) and to evaluate the values of the transport quantity (temperature), which are outside the range of specified boundary conditions at variously set calculation parameters.
Highlights
Aerodynamics deals with the movement of the air and the interaction between airflow and solid objects
The level of the physical accuracy of the numerical calculation is influenced by the mesh type, the choice of discretization schemes for the conversion of the general transport equations to the linear equations, and the choice of the calculating method of the transport quantity gradient ∇Φ
The scheme has the potential to improve the spatial accuracy for all types of grids by reducing the numerical diffusion and it is available for all transport equations
Summary
Aerodynamics deals with the movement of the air and the interaction between airflow and solid objects. The transport quantity does not have to be only the temperature, The solution of the problem is independent of the domain dimensions, gas density, and velocity It was verified on pilot calculations, whereby gradually changing all of these values in the thousands. The Ansys Fluent software uses the FVM to convert the general transport equations to the system of linear equations that are solved numerically by the Gauss–Seidel iteration method This solution consists in integrating the equations in each control volume (cell), where the result is the discrete equations presented the flow equilibrium (the conservation laws of the transport quantity Φ in given volume). The basic problem in the discretization of the advective term is the exact calculation of the transport quantity on the face of the specific volume Φf and its gradient ∇Φf. The gradients are necessary for the calculation of the scalar values on the cells faces for discretization the advective and for the diffusion term in the Equation (2)
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