Update README.md

README.md

@@ -1,10 +1,10 @@
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 license: cc-by-sa-4.0
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-SuperWing, a comprehensive benchmark dataset of transonic swept wings comprising 4239 wing shapes and near 30,000 flow fields across diverse geometries and
+SuperWing, a comprehensive benchmark dataset of transonic swept wings comprising 4239 wing shapes and nearly 30,000 flow fields across diverse geometries and
 operating conditions. Unlike previous efforts that rely on perturbations of a baseline wing, SuperWing is generated using a simplified yet expressive 
 parameterization scheme. By incorporating spanwise-varying dihedral, twist, and airfoil characteristics, the dataset captures realistic design complexity and 
-ensures greater diversity than existing ones. Please refer to our ![arXiv paper]{https://arxiv.org/abs/2512.14397} for more details on the dataset. 
+ensures greater diversity than existing ones. Please refer to our [arXiv paper](https://arxiv.org/abs/2512.14397) for more details on the dataset. 
 
 ![{DF9389F4-4D8B-4D16-A1E0-384D6E3F5847}](https://cdn-uploads.huggingface.co/production/uploads/6878e482bd4380c813fd99de/wL4x6q1tbNx1kjrexh5g5.png)
 
@@ -17,7 +17,7 @@ ensures greater diversity than existing ones. Please refer to our ![arXiv paper]
 # Data format:
 
 1. Geometric parameters
-   `config.dat` includes the basic shape parameters to build a wing from scratch, with the method detailed in our ![arXiv paper]{https://arxiv.org/abs/2512.14397}. For each wing
+   `config.dat` includes the basic shape parameters to build a wing from scratch, with the method detailed in our [arXiv paper](https://arxiv.org/abs/2512.14397). For each wing
    shape, we provide 8 operating conditions, but note that they are not exactly the operating conditions in the final dataset since some of them may not lead to convergent
    results.
    
@@ -50,12 +50,12 @@ ensures greater diversity than existing ones. Please refer to our ![arXiv paper]
    output for a machine learning model that predicts the aerodynamics of wings. 
 
    **reference mesh**: The simulation mesh on the wing surface is first interpolated to a reference mesh. In the spanwise ($j$-direction), 128 cross-sectional planes are
-   sampled with even spacing, and tips are excluded. For each cross-section ($i$-direction), a fixed set of normalized chordwise positions $\{(x/c)_i\}$ s is used for both 
+   sampled with even spacing, and tips are excluded. For each cross-section ($i$-direction), a fixed set of normalized chordwise positions $$\{(x/c)_i\}$$ s is used for both 
    the upper and lower surfaces, and the tail edge is represented only with one cell. The reference mesh along the wing surface is then unfolded as shown below, resulting 
    in a final vertex surface grid of $257 \times 129$ points per wing (`origingeom.npy`). This is useful when we need to calculate coefficients from the surface flow outputs.
-   The cell-centric grid for the mesh is obtained just by averaging the coordinates at the four vertices. 
+   The cell-centric grid for the mesh is obtained just by averaging the coordinates at the four vertices.
 
-   ![image](https://cdn-uploads.huggingface.co/production/uploads/6878e482bd4380c813fd99de/deWUNg0C2bxl7ZDQFfowu.png)
+   <img src="https://cdn-uploads.huggingface.co/production/uploads/6878e482bd4380c813fd99de/deWUNg0C2bxl7ZDQFfowu.png" alt="transform" width="40%">
 
 5. Raw solver output
    The raw output of surface flow (`surf.cgns`) and 3D volume fields (`vol.cgns`) is also available in their original formats (CGNS files with the ADF format). They need the