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Development of A Multiscale Flow Solver Using Wavelet Decomposition for Error Control, Grid Adaptation, and Flow Data Compression

机译:利用小波分解的多尺度流求解器的开发,用于误差控制,网格自适应和流数据压缩

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Current state-of-the-art flow simulations rely on four major techniques (finite difference, finite volume, finite element, or discontinuous galerkin methods) to solve flow equations. The methodologies are performing very well for medium size flow problems, but their performance drops appreciably for very large size flow problems (>1 billion cells). This is partly caused by the limitation of the hardware/software to handle monumental amount of data generated by these billion computational cells. However, most of the flow solutions may not require all of these billion cells to provide sufficient accuracy. The fundamental flaw is the lack of efficient grid adaptation capability that can maintain specified error limit while minimizing computational resources. Oftentimes, the adapted grid is optimal for certain variables at specific scales but sub-optimal for others, which leads to unnecessary increase in numbers of computational variables after the adaptation cycle. To remedy this problem, a new paradigm for flow solver is developed with capabilities to optimally compress flow data and identify/resolve flow features at various scales of interest while maintaining accuracy. This is achieved through the development of a novel multi-scale flow solver that applies wavelet decomposition of the flow variables to provide optimal error control and grid adaptation capabilities as well as flow data compression. The wavelet solver is developed using finite difference and finite volume approaches to solve linear and non-linear 1D partial differential equations. Varieties of algorithms, boundary conditions, initial conditions are used to demonstrate its versatility and flexibility. The results showed that the wavelet solver was capable of providing significant compression (averaging between 70-90%) in flow data, while maintaining solution accuracy and adaptively resolving multi-scale flow features. The numerical error could be controlled by adjusting an error threshold limit, which dictated the amount of data compression and multi-scale adaptivity necessary to maintain the error. It was also observed that the wavelet compression did not alter the error characteristic of the underlining scheme.
机译:当前最新的流动模拟依赖于四种主要技术(有限差分,有限体积,有限元或不连续galerkin方法)来求解流动方程。这些方法对于中等大小的流量问题表现很好,但是对于非常大的大小流量问题(> 10亿个单元),它们的性能会明显下降。部分原因是由于硬件/软件的限制,无法处理由这十亿个计算单元生成的大量数据。但是,大多数流动解决方案可能并不需要所有这些十亿个单元来提供足够的精度。基本缺陷是缺乏有效的网格自适应功能,该功能无法在最小化计算资源的同时保持指定的错误限制。通常,对于特定比例下的某些变量,自适应网格是最佳的,而对于其他比例而言,自适应网格则次优,这会导致在自适应周期后不必要地增加计算变量的数量。为了解决这个问题,开发了一种新的流量求解器范例,它具有在保持精度的同时以最佳比例压缩流量数据并识别/解析各种关注尺度的流量特征的能力。这是通过开发新型多尺度流求解器来实现的,该求解器对流变量进行小波分解,以提供最佳的误差控制和网格自适应功能以及流数据压缩。小波求解器是使用有限差分和有限体积方法开发的,用于求解线性和非线性一维偏微分方程。各种算法,边界条件,初始条件用于证明其多功能性和灵活性。结果表明,小波求解器能够在流量数据中提供显着的压缩效果(平均在70%到90%之间),同时保持求解精度并自适应地解析多尺度流量特征。可以通过调整错误阈值限制来控制数字错误,该阈值决定了维持该错误所需的数据压缩量和多尺度适应性。还观察到小波压缩并没有改变下划线方案的误差特性。

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