CFD非结构化网格流场体可视化方法研究
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摘要
体可视化是目前公认的3D标量场可视化的最重要途径。它通过“重采样”与“图像合成”等步骤，直接将由离散的3D数据场生成屏幕图像，能够使用户看穿数据体，深入了解数据场的全局状态和内部细节，在流场可视化中的地位举足轻重。与结构化网格相比，非结构化网格拓扑结构复杂，导致体可视化算法设计和实现困难，时空复杂性高。尤其是，对于CFD数值模拟产生的3D非结构化网格流场数据，还具有数据格式多样、物理特征复杂以及非定常（时变）等特点。复杂的数据对象使已有的体可视化技术在精确性、有效性、实时性等方面面临严峻挑战。本课题面向CFD领域的实际应用需求，针对已有非结构化网格体可视化方法存在的不足之处，深入研究了格心格式数据的高精度绘制、重要物理特征的准确绘制、非结构化网格体数据的清晰绘制、非定常流场体数据的高效绘制等目前流场体可视化中的多个热点和难点问题。所完成的主要工作和创新成果有：
1．针对已有可视化方法只能对CFD非结构化网格格心格式数据完成“间接”绘制而导致的精度和矛盾问题，提出一种非结构化网格格心格式数据直接体可视化方法。该方法直接基于原始格心数据完成数据重构，避免了外推计算，能够获得精度较高的绘制数据；在此基础上，结合迎风型FVM求解思想和Roe平均方法，设计了一种基于双控制体的采样点间断态重构方法，将数值解中的“流间断”信息传递给绘制数据，解决已有可视化方法与数值计算方法的矛盾问题。误差分析和实验结果表明，该方法能明显提高数据重构精度，使绘制结果与数值计算结果更为一致。同时，该方法的有效性并不局限于体绘制，对于其他可视化方法（如等值面提取、流线跟踪等）也同样适用。
2．针对已有3D激波特征提取方法准确性、有效性和适应性差的问题，提出一种非结构化网格流场3D激波特征体可视化方法。该方法利用激波物理特性，结合光线投射体绘制算法优势，基于两级采样计算完成3D激波检测和噪声过滤；在激波检测时，基于压力梯度计算一级采样点处流场的正则马赫数，有效排除了接触间断特征；在此基础上，通过比较二级采样点处流场速度在激波切面上的分量大小来实现噪声的自动识别与过滤，使过滤的有效性不依赖于数据集本身；针对拓扑复杂的3D非结构化网格数据，设计实现了基于GPU的激波特征高效体绘制算法。实验结果表明，该方法具有良好的有效性和适应性，即便对包含多激波特征的复杂流场数据，也具有很高的准确性。
3．针对3D非结构化网格数据采样点梯度计算复杂而导致体光照算法设计和实现困难、实时性差的问题，提出一种高效的非结构化网格数据体光照计算与实现方法。该方法基于格林公式和反转距离外推（或体积加权外推）计算非结构化网格顶点梯度，对于不同类型的非结构化网格单元都具有较高的准确性和良好的适应性；在此基础上，采用单元梯度张量计算采样点梯度，有效降低了计算开销；设计了纹理数据结构，实现了基于GPU的实时体光照算法。实验结果表明，所提出的3D非结构化网格数据体光照方法，能够更加清晰地表现3D流场的局部细节和层次结构；且对较大规模非结构化网格体数据，绘制性能可达到实时交互。
4．．针对3D非结构化网格时变流场数据时空一致性不能有效利用而导致动态体绘制时空效率较差的问题，提出一种基于时空一致性的非结构化网格时变流场高效体绘制方法。该方法在分析非结构化网格单元和顶点数据时间一致性的基础上，建立单元和顶点数据时间表，充分利用时间表中的时间一致性信息降低动态采样计算开销；考虑面相邻单元数据的空间一致性，加速光线在数据体中的穿越过程；设计了一种单元和顶点数据相分离的GPU纹理结构以及一种小巧的单元梯度矩阵，明显降低了显存开销；设计了以16步时变数据为单位的数据分组与调度策略，既有效了避免绘制停顿，又使显存纹理结构更为紧致、高效。空间分析和实验表明，该方法不仅明显提高了绘制效率，而且具有更优显存空间利用率，能实现更大网格规模的非结构化网格时变流场体绘制。
Volume visualization, which plays an important role in flow visualization, hasbeen taken as the leading and preferred method to visualize 3D scalar fields. It producesthe final image from the discrete 3D fields by re-sampling and synthesizing, makingusers gain a direct insight into the whole state and the details of the fields. Compared tostructured-grid data, unstructured-grid data with complicated topology result indifficulties in designing and implementing the volume visualization algorithms,especially for the 3D unstructured-grid flow fields from the CFD simulation. It is achallenging work to achieve the accurate, available and real-time visualization of the 3Dunstructured-grid flows with different formats, complicated physical features andunsteady behaviors. To overcome the deficiencies of the existing volume visualizationmethods for the 3D unstructured-grid flows, this dissertation focuses on the followingissues in the practical CFD applications: high-accuracy visualization of the cell-centereddata, exact extraction of the important physical features, volume illumination of the 3Dunstructured-grid data and efficient rendering of the unsteady flows. The majorcontributions of this paper are as follows.
1. To visualize unstructured cell-centered data, the existing methods can onlyperform indirect visualization, which depress the rendering accuracy and violate thediscontinuity constraint. To solve the problems, this paper proposes a direct method tovisualize unstructured cell-centered data. High accuracy is achieved via datareconstruction performed directly on the original cell-centered data. To keep thediscontinuity, the field at a sample is reconstructed using the double control volumesand the Roe-average computation inspired by an Upwind-FVM solver. Analysis andexperiments demonstrate that the proposed approach gains a high-accuracyreconstruction which is more accordant with the numerical solution. In addition, theidea of direct reconstruction is not only fit for volume rendering, but also can be appliedto other visualization methods (such as isosurface extraction and streamline tracking)and helps render high-accuracy images for CFD simulation.
2. To deal with the accuracy, availability and adaptability deficiency of the existingmethods on extracting the 3D shocks in flows, a two-level sampling method ispresented for shock detection and noise filtering based on the shock attributes with theaid of ray casting. The normal Mach at the first-level sample is computed with thepressure gradient to detect the shock and the contact discontinuity feature is eliminatedaccordingly. To identify and filter the noise, the velocity magnitude at the second-levelsample is projected on the tangent of the shock to evaluate the noise, which isindependent of the data set. This work is performed on GPU for the 3D unstructuredgriddata with complicated topology. Experimental results show that the approach can automatically filter the noise. The adaptability and accuracy are much better than theexisting methods even for the multi-shock flows.
3. It is difficult to estimate the sample gradient for unstructured-grid volumeillumination due to the complicated topology, which makes the real-time volumeillumination be hardly achieved because of the computation complexity and thedifficulty of implementation on GPU. This paper proposes an efficient illuminationcomputation and implementation approach for unstructured-grid volume. The vertexgradient is accurately estimated using the Green-Gauss theorem and the inverse-distanceextrapolation (or the volume-weighted extrapolation), which can be applied to theunstructured cells with various shapes. Furthermore, the sample gradient is obtained byan efficient method based on the cell gradient tensor and the computation cost islowered consequently. With the aid of a well-designed data structure, the real-timeperformance of the algorithm can be achieved on GPU even for the large data sets.Experiments show that this approach can lead to a clear insight into the details andstructures of the 3D flows.
4. Although the temporal and spatial coherence plays an essential role invisualizing unstructured time-varying fields, the existing approaches do not pay enoughattention to it and thus depresses the performence. This paper presents an efficientapproach for volume rendering of unstructured time-varying flows by utilizing thetemporal and spatial coherence. The temporal coherence of both the cell and the vertexdata is analyzed to build the temporal tables, which is used to accelerate the dynamic resampling.The spatial coherence between the face-adjacencies is exploited to speed upthe ray traversal. We also design a novel texture structure that separates the vertex datafrom the cell data and a smart gradient matrix to reduce the pressure of GPU memory. Abasic unit containing 16-step data is used in data compression and management to avoidrendering stalls and lead to a compact and efficient storage. Analysis and experimentsdemonstrate that the approach gains a much lower cost of both time and space than theexisting methods, which allows rendering time-varying data on a larger mesh scale inreal time.
1．针对已有可视化方法只能对CFD非结构化网格格心格式数据完成“间接”绘制而导致的精度和矛盾问题，提出一种非结构化网格格心格式数据直接体可视化方法。该方法直接基于原始格心数据完成数据重构，避免了外推计算，能够获得精度较高的绘制数据；在此基础上，结合迎风型FVM求解思想和Roe平均方法，设计了一种基于双控制体的采样点间断态重构方法，将数值解中的“流间断”信息传递给绘制数据，解决已有可视化方法与数值计算方法的矛盾问题。误差分析和实验结果表明，该方法能明显提高数据重构精度，使绘制结果与数值计算结果更为一致。同时，该方法的有效性并不局限于体绘制，对于其他可视化方法（如等值面提取、流线跟踪等）也同样适用。
2．针对已有3D激波特征提取方法准确性、有效性和适应性差的问题，提出一种非结构化网格流场3D激波特征体可视化方法。该方法利用激波物理特性，结合光线投射体绘制算法优势，基于两级采样计算完成3D激波检测和噪声过滤；在激波检测时，基于压力梯度计算一级采样点处流场的正则马赫数，有效排除了接触间断特征；在此基础上，通过比较二级采样点处流场速度在激波切面上的分量大小来实现噪声的自动识别与过滤，使过滤的有效性不依赖于数据集本身；针对拓扑复杂的3D非结构化网格数据，设计实现了基于GPU的激波特征高效体绘制算法。实验结果表明，该方法具有良好的有效性和适应性，即便对包含多激波特征的复杂流场数据，也具有很高的准确性。
3．针对3D非结构化网格数据采样点梯度计算复杂而导致体光照算法设计和实现困难、实时性差的问题，提出一种高效的非结构化网格数据体光照计算与实现方法。该方法基于格林公式和反转距离外推（或体积加权外推）计算非结构化网格顶点梯度，对于不同类型的非结构化网格单元都具有较高的准确性和良好的适应性；在此基础上，采用单元梯度张量计算采样点梯度，有效降低了计算开销；设计了纹理数据结构，实现了基于GPU的实时体光照算法。实验结果表明，所提出的3D非结构化网格数据体光照方法，能够更加清晰地表现3D流场的局部细节和层次结构；且对较大规模非结构化网格体数据，绘制性能可达到实时交互。
4．．针对3D非结构化网格时变流场数据时空一致性不能有效利用而导致动态体绘制时空效率较差的问题，提出一种基于时空一致性的非结构化网格时变流场高效体绘制方法。该方法在分析非结构化网格单元和顶点数据时间一致性的基础上，建立单元和顶点数据时间表，充分利用时间表中的时间一致性信息降低动态采样计算开销；考虑面相邻单元数据的空间一致性，加速光线在数据体中的穿越过程；设计了一种单元和顶点数据相分离的GPU纹理结构以及一种小巧的单元梯度矩阵，明显降低了显存开销；设计了以16步时变数据为单位的数据分组与调度策略，既有效了避免绘制停顿，又使显存纹理结构更为紧致、高效。空间分析和实验表明，该方法不仅明显提高了绘制效率，而且具有更优显存空间利用率，能实现更大网格规模的非结构化网格时变流场体绘制。
Volume visualization, which plays an important role in flow visualization, hasbeen taken as the leading and preferred method to visualize 3D scalar fields. It producesthe final image from the discrete 3D fields by re-sampling and synthesizing, makingusers gain a direct insight into the whole state and the details of the fields. Compared tostructured-grid data, unstructured-grid data with complicated topology result indifficulties in designing and implementing the volume visualization algorithms,especially for the 3D unstructured-grid flow fields from the CFD simulation. It is achallenging work to achieve the accurate, available and real-time visualization of the 3Dunstructured-grid flows with different formats, complicated physical features andunsteady behaviors. To overcome the deficiencies of the existing volume visualizationmethods for the 3D unstructured-grid flows, this dissertation focuses on the followingissues in the practical CFD applications: high-accuracy visualization of the cell-centereddata, exact extraction of the important physical features, volume illumination of the 3Dunstructured-grid data and efficient rendering of the unsteady flows. The majorcontributions of this paper are as follows.
1. To visualize unstructured cell-centered data, the existing methods can onlyperform indirect visualization, which depress the rendering accuracy and violate thediscontinuity constraint. To solve the problems, this paper proposes a direct method tovisualize unstructured cell-centered data. High accuracy is achieved via datareconstruction performed directly on the original cell-centered data. To keep thediscontinuity, the field at a sample is reconstructed using the double control volumesand the Roe-average computation inspired by an Upwind-FVM solver. Analysis andexperiments demonstrate that the proposed approach gains a high-accuracyreconstruction which is more accordant with the numerical solution. In addition, theidea of direct reconstruction is not only fit for volume rendering, but also can be appliedto other visualization methods (such as isosurface extraction and streamline tracking)and helps render high-accuracy images for CFD simulation.
2. To deal with the accuracy, availability and adaptability deficiency of the existingmethods on extracting the 3D shocks in flows, a two-level sampling method ispresented for shock detection and noise filtering based on the shock attributes with theaid of ray casting. The normal Mach at the first-level sample is computed with thepressure gradient to detect the shock and the contact discontinuity feature is eliminatedaccordingly. To identify and filter the noise, the velocity magnitude at the second-levelsample is projected on the tangent of the shock to evaluate the noise, which isindependent of the data set. This work is performed on GPU for the 3D unstructuredgriddata with complicated topology. Experimental results show that the approach can automatically filter the noise. The adaptability and accuracy are much better than theexisting methods even for the multi-shock flows.
3. It is difficult to estimate the sample gradient for unstructured-grid volumeillumination due to the complicated topology, which makes the real-time volumeillumination be hardly achieved because of the computation complexity and thedifficulty of implementation on GPU. This paper proposes an efficient illuminationcomputation and implementation approach for unstructured-grid volume. The vertexgradient is accurately estimated using the Green-Gauss theorem and the inverse-distanceextrapolation (or the volume-weighted extrapolation), which can be applied to theunstructured cells with various shapes. Furthermore, the sample gradient is obtained byan efficient method based on the cell gradient tensor and the computation cost islowered consequently. With the aid of a well-designed data structure, the real-timeperformance of the algorithm can be achieved on GPU even for the large data sets.Experiments show that this approach can lead to a clear insight into the details andstructures of the 3D flows.
4. Although the temporal and spatial coherence plays an essential role invisualizing unstructured time-varying fields, the existing approaches do not pay enoughattention to it and thus depresses the performence. This paper presents an efficientapproach for volume rendering of unstructured time-varying flows by utilizing thetemporal and spatial coherence. The temporal coherence of both the cell and the vertexdata is analyzed to build the temporal tables, which is used to accelerate the dynamic resampling.The spatial coherence between the face-adjacencies is exploited to speed upthe ray traversal. We also design a novel texture structure that separates the vertex datafrom the cell data and a smart gradient matrix to reduce the pressure of GPU memory. Abasic unit containing 16-step data is used in data compression and management to avoidrendering stalls and lead to a compact and efficient storage. Analysis and experimentsdemonstrate that the approach gains a much lower cost of both time and space than theexisting methods, which allows rendering time-varying data on a larger mesh scale inreal time.
引文
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