有限體積法(FVM)的應用在計算流體力學中有普遍增加的趨勢。其中有許多方法專注於通量計算，像是早期的平衡通量法(Equilibrium Flux Method, EFM)，其通量計算是經由積分速度機率分佈函數而取得。然而，在數值計算中會產生指數函數與誤差函數，在計算上這不僅費時並且還有可能導致截斷誤差的發生。本研究的目的在於探討三角化平衡通量法(Triangular Equilibrium Flux Method, TEFM)，此方法利用較為簡單的分佈函數總和近似馬克斯威爾-波茲曼速度機率分佈，進而取代原本計算昂貴的方程式，並使用MPI與A系列的AMD APU於平行計算中。為了要進一步提高計算效能，使用多重圖型處理器(MPI-CUDA)平行模式以達更高的模擬效率。透過已存在的數值模擬結果，來驗證一階與二階空間精準度的差別與正確性。

Kinetic-theory based Finite Volume Methods (FVM) have become increasingly common in Computational Fluid Dynamics (CFD). Many of these methods focus on computation of fluxes through integrating a velocity probability distribution function, such as the early Equilibrium Flux Method (EFM). However, analytical computation of these moments results in the exponential function and error function which is not only time-consuming but may also introduce error through truncation. The purpose of this study is to investigate an alternative – the Triangular Equilibrium Flux Method (TEFM) which uses the sum of simpler distribution functions to approximate the Maxwell-Boltzmann equilibrium velocity probability distribution function – applied to parallel computing using MPI with a specific focus on the A-series of AMD APU’s. To further enhance the performance, the hybrid MPI-CUDA parallelization paradigm is employed with multiple GPUs to achieve higher simulation efficiency. Furthermore, several benchmarks are used to verify both first and second order numerical results

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