Reduction of Numerical Diffusion in FFD Model

Abstract

Fast flow simulations are needed for some applications in building industry, such as the conceptual design of indoor environment or teaching of Heating Ventilation and Air Conditioning (HVAC) system design in classroom. Instead of pursuing high accuracy, those applications require only conceptual distributions of the flow but within a short computing time. To meet these special needs, a Fast Fluid Dynamics (FFD) method was proposed to provide fast airflow simulation with some compromise in accuracy. This study is to further improve the FFD method by reducing the numerical viscosity that is caused by a linear interpolation in its semi-Lagrangian solver. We propose a hybrid scheme of a linear and a third-order interpolation to reduce the numerical diffusion in low order scheme and the numerical dispersion in high order scheme. The FFD model with both linear and hybrid interpolations are evaluated by simulating four different indoor flows. The results show that the hybrid interpolation can significantly improve the accuracy of the FFD model with a small amount of extra computing time.

A high‐order backward forward sweep interpolating algorithm for semi‐Lagrangian method

“…(2) into three sub-equations by using a fractional step method [7,8,15]: (2) into three sub-equations by using a fractional step method [7,8,15]:…”

“…The major benefit of using the semi-Lagrangian method is its unconditional stability even for large time steps, thus offering faster solution than other computational fluid dynamics solvers. This whole solution procedure is named 'fast fluid dynamics' (FFD) by some researchers [7,9,16]. the diffusion and source term, the advection term, and the pressure gradient term [8,15].…”

“…poor conservation of advected properties and/or high numerical dissipations [7,17]. It is assumed that fluid properties remain constant along the characteristic curve of the flow within one time-step.…”

“…Because a departure point is often located differently from Eulerian grids, e.g. While these methods tried to improve the accuracy in different ways, they also add complexity and extra computational cost to the semi-Lagrangian method [7]. Low-order interpolation schemes thus often cause inaccurate predictions of fluid properties, which is consequently a major source for the well-known drawbacks of the method: e.g.…”

“…cell centers, an interpolation algorithm is needed to find the properties at the departure point by using the neighboring Eulerian cells. Therefore, Zuo et al [7] developed a relatively simple hybrid method by combining a linear and third-order backward interpolation schemes: using linear interpolation near the sharp gradient to reduce dispersion errors and using the third-order interpolation in other regions to reduce numerical dissipations. poor conservation of advected properties and/or high numerical dissipations [7,17].…”