Large-Scale Unstructured Unsteady Flow

Version	Summary	Created by	Modification	Content Size	Created at	Operation
1		Xiaokun Tian	--	1809	2023-11-28 01:30:55	\|
2	update references and layout	Rita Xu	Meta information modification	1809	2023-11-28 02:26:05	\|

This entry is adapted from the peer-reviewed paper 10.3390/app132112062

Animation visualization is one of the primary methods for analyzing unsteady flow fields. Loading and rendering individual time steps sequentially can result in substantial frame delay, whereas loading and rendering all time steps simultaneously can result in excessive memory usage.

unsteady flow flow animation unstructured mesh

1. Introduction

CFD (computational fluid dynamics) is a numerical simulation technique used to study fluid motion, heat transmission, and other phenomena by approximating complex flow field problems with a finite number of discrete points ^[1]. Numerous scientific phenomena are time-dependent, such as the development of thunderstorms, the combustion of substances, and the movement of ocean currents. The distribution of flow field characteristics corresponding to these conditions is related to both spatial and temporal variations. CFD simulations of time-dependent phenomena will produce a series of time-continuous flow field data, also known as unsteady flow field data.

Typically, geometry modeling, mesh generation, and numerical solution are required to obtain simulated data for the flow field problem during the CFD simulation process. Finally, scientific visualization techniques are used to graphically represent the flow field characteristics encoded within the simulated data. Flow field data can be categorized as structured mesh, unstructured mesh, or hybrid mesh data based on the various mesh generation methodologies. Unstructured meshes do not have mathematically logical connections between their internal nodes. They have high generalizability, strong adaptability to regions with intricate flow fields, and flexible mesh generation. Using mesh adaptive refinement, they can increase the computational accuracy of specific regions and have been increasingly used to solve increasingly complex engineering problems. Unsteady flow field data based on unstructured meshes is now a crucial and common type of flow field data for the investigation of complex time-varying phenomena. The data scale grows massively over time, which impedes the visualization and analysis of the unsteady flow field data. Data I/O delay, slow rendering, and inefficient interaction response are some of the main difficulties. Therefore, effective visualization techniques are needed to analyze such flow field data.

Animation visualization is a general-purpose technique for displaying time series data and an essential technique for displaying unsteady flow fields. It imports and draws the flow field data of each time step in chronological order, forming an unsteady animation ^[2], and then displays the spatiotemporal characteristics of the unsteady flow field in animation form in a more comprehensive manner ^[3]. Unlike traditional animation, animation visualization does more than play pictures composed of pixels one after the other. Fundamental computer graphic elements like triangles form the base for animation visualization. The flow field mesh is rendered for display via graphic elements in flow field visualization. This rendering method can make use of computer graphic techniques like transformation matrices, which let the user manipulate the flow field image by panning, zooming, reflecting, and so on. Furthermore, the distribution of the flow field’s physical quantities is represented by the values of the variables dispersed across the mesh. It allows the user to color the flow field mesh according to the scalar values of the variables and can also calculate to generate other graphs, such as isosurfaces. Users can interact in real time at any point during the animation visualization with the support of visualization techniques and flow field data. The rendering pipeline creates new images in real time based on the interaction parameters whenever the user interacts, for example, by rotating, panning, or changing the coloring variables. As a result, the animation visualization can offer a comprehensive study of the unsteady flow field. However, the application of animation visualization to unstructured unsteady flow fields still faces the following issues: (1) Each frame of the animation must acquire the flow field topology and variable information corresponding to the time step. Reading and constructing the unstructured mesh from the data file is a lengthy process due to the complexity and diversity of the unstructured mesh’s topological elements. Therefore, loading each time step separately will result in a significant interframe delay ^[4]. (2) The number of flow field meshes and the temporal resolution (number of time steps) are increasing as a result of the continuous enhancement of computer hardware and software performance, which is resulting in an increase in the scale of CFD simulation data. Consequently, a single time step of flow field meshes can reach millions or even billions of elements and the time steps can be hundreds or thousands, making it challenging for common computers to load all time steps into memory for visual analysis.

2. Unsteady Data Compression

Memory optimization is primarily focused on the spatial consistency within a single time step and the temporal consistency between continuous time steps in order to compress data for an unsteady flow field with temporal and spatial dimensions. Shen et al. ^[5] designed a time-space partitioning (TSP) tree that divides the spatial domain into an octree as the primary structure, then divides the temporal domain into a binary time tree as the secondary structure and uses the data in the adjacent spatiotemporal domain to represent the current data based on the error tolerance. Du et al. ^[6] proposed a space-partitioning time (spt) tree, which first divides the temporal domain into a fully balanced binary time tree as a primary structure and then divides the spatial domain into a standard complete octree, obtaining a higher data reuse rate because unsteady data exhibits a stronger correlation in time. Ma et al. ^[7] used temporal consistency to prune tree nodes by storing each time step of data in an octree form separately and then comparing the similarity of adjacent time step data for pruning. The kind of method that separates the temporal and spatial dimensions and uses differential coding and octree to compress unsteady data by using temporal and spatial correlation, respectively, can reorganize the original data into a multi-resolution hierarchy, which has a faster encoding and decoding speed and higher compression ratio. The accuracy loss caused by compression is small ^[8], so it is widely used in unsteady data visualization. Generalizing existing research to unstructured unsteady flow fields is challenging. Most existing research relies on structured unsteady data. Thus, the regular hexahedral mesh can use octree to represent the mesh distribution in eight directions accurately ^[9]. Moreover, it can efficiently calculate differential coding under a certain premise. The premise is that the flow field meshes do not change with time; only the flow field variables change with time. However, unstructured unsteady flow fields are different. They have some challenges that make it difficult to explicitly represent hierarchical structures. They have an irregular mesh distribution and multi-density characteristics. The meshes and variables of the flow field will change over time. If structured meshes are used to represent unstructured flow fields and then spatiotemporal domain partitioning is performed, there are issues such as mesh partitioning density affecting data accuracy, difficulty in fitting complex unstructured mesh structures, and an inability to correspond vertex data accurately. Therefore, compressing unstructured meshes into structured meshes is challenging. It is possible to attempt to design adaptive octrees using leaf nodes of different densities to represent an unstructured triangular mesh with an irregular mesh density distribution. But, it is challenging to design compression algorithms that correspond to mesh spatial positions in different time steps.

In addition to the aforementioned compression techniques that separate the temporal and spatial dimensions, there are also compression techniques that regard the entire unsteady data set as four-dimensional data and extend the three-dimensional volume data compression techniques to four-dimensional space compression. Ibarria et al. ^[10], for instance, proposed a high-dimensional data compression method that combines volume texture compression (VTC) and the Lorenzo high-dimensional parallelogram predictor, which uses the temporal and spatial correlation of time-varying data to predict the current voxel value from the decompressed adjacent voxel data values. Linsen et al. ^[11] proposed a partitioning method based on the fourth root of 2 to divide unsteady data into fine-grained hierarchical data, sampling and approximating each detail level with biquadratic B-spline wavelets. Wilhelms et al. ^[12] proposed a method for encoding unsteady data using four-dimensional trees, with each node containing the data model below it, the error and evaluation information of selective traversal, and the structural information. These techniques have a high compression ratio, little accuracy loss, and can make good use of the correlation between adjacent time steps. However, during decompression, they heavily rely on neighboring time steps, which leads to high time and space overhead. Data compression can significantly reduce the amount of data that must be loaded into memory, but it also introduces a data decompression process during animation playback, which adds to the animation’s interframe delay. Additionally, the majority of four-dimensional compression techniques currently in use are based on structured meshes, which makes them challenging to adapt to complex unstructured data.

3. Animation Inter-Frame Delay Optimization

Typically, the method of reading and rendering while playing an unsteady animation is used to increase resource utilization. The rendering process can be accelerated by the use of multithreading, GPU encoding, and other techniques ^[13]^[14]. Mensmann et al. ^[15] implemented a CPU-GPU hybrid decompression that conducted LZO lossless decompression on the CPU, followed by variable-length coding decompression and differential decompression on the GPU, thereby decreasing the time overhead of data decompression. Chiueh et al. ^[16] proposed a pipeline rendering method for unsteady data that alternates the execution of the data I/O process and the rendering and drawing process, thus concealing the data reading overhead. Nevertheless, the data I/O time will be much greater than the rendering time when a lot of data is processed in a single time step. Creating a pipeline is challenging due to the performance bottleneck in loading data from external memory, which necessitates the use of additional processors for parallel processing. Yu et al. ^[17] designed a parallel architecture pipeline for unsteady data, which can be used for interactive visualization of large-scale seismic simulation data, but this parallel design requires the support of a supercomputer’s multi-processor and high memory capacity and is therefore incompatible with ordinary computers. Therefore, when the size of the unsteady data is large, there is not yet a general data processing method that enables standard personal computers to play unsteady animation smoothly.

To handle large-scale unstructured unsteady data, most of the current state-of-the-art commercial visualization software, for example, Tecplot 360 EX 2022 R1 and VisIt 3.3.0, employ high-performance computing methods ^[18]. They avoid using data compression techniques to render the animation, in order to preserve the data accuracy. By adopting a server–client architecture, they distribute visualization computing tasks to multiple nodes and leverage parallel computing to the fullest. This approach enables interactive animation of large-scale unstructured unsteady flow fields, but it is costly due to the high demand for hardware resources. Data compression methods based on tree structures and differential coding can save memory, but they are not easy to apply to irregular unstructured unsteady flow fields. Furthermore, these methods increase CPU loads on personal computers. They need extra data decompression or specific rendering algorithms for the compressed data, which lowers their generality.

References

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Xiaokun Tian

Chao Yang

Yadong Wu

Zhouqiao He

Yan Hu

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Update Date: 28 Nov 2023

Table of Contents

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1. Introduction

2. Unsteady Data Compression

3. Animation Inter-Frame Delay Optimization

References