LiDAR sensors provide rich 3D information about their surrounding{s} and are becoming increasingly important for autonomous vehicles tasks such as {localization}, semantic segmentation, object detection, and tracking. {Simulation} accelerates the testing, validation, and deployment of autonomous vehicles while {also} reducing cost and eliminating the risks of testing in real-world scenarios. We address the problem of high-fidelity LiDAR simulation and present a pipeline that leverages real-world point clouds acquired by mobile mapping systems. Point-based geometry representations, more specifically splats {(2D oriented disks with normals)}, have proven their ability to accurately model the underlying surface in large point clouds{, mainly with uniform density}. We introduce an adaptive splat generation method that accurately models the underlying 3D geometry {to handle real-world point clouds with variable densities}, especially for thin structures. Moreover, we introduce a {fast} LiDAR {sensor} simulator, {working} in the splatted model, {that leverages} the GPU parallel architecture with an acceleration structure while focusing on efficiently handling large point clouds. We test our LiDAR simulation in real-world conditions, showing qualitative and quantitative results compared to basic splatting and meshing techniques, demonstrating the interest of our modeling technique.