Fig. 1. (a) Ray trajectories through cells: one follows the cell-AVG curved path, and the other represents the cell-confined RK straight-line path. (b) A spherical target represented in 2D cylindrical coordinates and spherical coordinates. (c) Truncated-wedge cells derived from 2D cylindrical or spherical grids, lifted into a temporary 3D space for ray tracing.

Fig. 2. (a) Power partitioning of the laser focal spot. Intersection points (marked with ‘+’) of rays with (b) rectangular, (c) cylindrical and (d) spherical computational domains between the lens and focal planes.

Fig. 3. (a) Intersection of the connecting line with a cylindrical surface, where and are projected onto the solution plane followed by a Z-rotation. (b) Intersection of the connecting line with a spherical surface, where and are mapped to the solution plane through a Z-rotation followed by a Y-rotation. (c) In solution plane, the line connecting and is parallel to the X-axis, enabling straightforward calculation of the intersection point coordinates.

Fig. 4. (a) Bilinear interpolation for interior point ’s value and spatial derivatives. Region dimensions are , with coordinates (origin at the lower-left corner). Here, represents cell vertex values and are edge-centered gradients. (b) Vertex values and edge gradients are derived from known cell-centered values .

Fig. 5. Comparison of linear interpolation and cubic interpolation methods for constructing internal field values and gradient values of a rarefaction wave.

Fig. 6. Ray reflection at a sharp interface. The lower part represents the high-density target. Here, is the incident velocity, the overshoot velocity, the corrected velocity and the ejection velocity.

Fig. 7. Possible scenarios of ray segments intersecting 2D fluid cells under the constraint. Rectangular faces are shown, but sphere/cylinder faces are also applicable.

Fig. 8. One-dimensional energy deposition rasterization allocation process.

Fig. 9. Two-dimensional energy deposition rasterization process.

Fig. 10. Plasma Luneburg lens parameters and ray trajectories.

Fig. 11. (a) Ray impact points near the focus. Shown are 32 rays per beam. (b) Error in impact point distribution versus cell grid spacing.

Fig. 12. (a) Density and (b) flow velocity distributions of rarefied step-profile plasma. (c) Doppler frequency shifts during ray traversal through plasma. (d) Fluid domain light intensity. (e) Fluid domain frequency shift.

Fig. 13. Laser-driven spherical water vapor target in cylindrical coordinates: (a) initial density distribution, half-space mirrored; (b) 3D ray trajectories recorded in Cartesian coordinates; (c) laser volumetric heating power; (d) density distribution at .