Abstract
A compact and accurate discretization for fluid flow simulations is introduced in this paper. Contrary to the common wisdom in a convectional scheme, the solution gradient required for a high-resolution scheme is provided by solving its corresponding difference equation rather than by interpolation from solution values at neighboring computational nodes. To achieve this goal, a supplementary equation and its associated control volume are proposed to retain a compact and accurate discretization. Scheme essentials are exposed by numerical analyses on simple one-dimensional modeled problems to reveal its formal accuracy. Several test problems are solved to illustrate the feasibility of present formulation. From the obtained numerical results, it is evident that the proposed scheme will be a useful tool to simulate fluid flow problems in arbitrary domains.
Highlights
To provide a feasible simulation tool for incompressible flow in a complicated domain, we have successfully developed associated solution procedures on arbitrary LagrangianEulerian (ALE) [1, 2] and subsequently staggered triangular grid systems [3, 4]
We have successfully developed a feasible solution procedure to simulate incompressible fluid flow in complicated domains
It is put into effect by discretizing the incompressible Navier-Stokes equations with primitive variables on staggered polygonal grids
Summary
To provide a feasible simulation tool for incompressible flow in a complicated domain, we have successfully developed associated solution procedures on arbitrary LagrangianEulerian (ALE) [1, 2] and subsequently staggered triangular grid systems [3, 4]. (3) Its accuracy heavily depends upon grid arrangement To circumvent these inconveniences, we will employ an alternative approach to determine the solution gradient: it should be directly calculated by solving its corresponding governing equation just as the solution variable. We will employ an alternative approach to determine the solution gradient: it should be directly calculated by solving its corresponding governing equation just as the solution variable In this way, the characteristics pertaining to the governing equation can be directly deliberated in the solution gradient and increase the simulation accuracy. The characteristics pertaining to the governing equation can be directly deliberated in the solution gradient and increase the simulation accuracy To achieve this goal, the present paper is designed to unveil the underlying basics to be used in fluid flow problems. Detailed descriptions on associated formulation fundamentals, numerical analyses, solution procedure and more extensive validations can be consulted in our previous work [9,10,11,12,13]
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