3D Meshless Detonation Front Resetting with Surface Huygens Construction

A detonation front can be expressed by a set of moving particles. Local front geometry can be computed with interpolation of curved front fitting which provides front curvature. The difference between normal velocities between consecutive time steps provides front acceleration. With a given DSD (detonation-shock-dynamics) evolution law for a specified explosive and a given initial detonation front, the motion of a detonation in this explosive can be predicted by the motion of the particles explicitly. The LLNL meshfree DSD tracking package SDOT is developed taking this approach.



A major issue with a moving front expressed by particles is, when a front is compressed / stretched in evolution, the particle spacing is not expected to maintain consistency. Furthermore, when interacting with the boundary or another front, some particles on a given front become invalid and must be removed. A method to reset a pointy spatial surface must be employed to maintain the quality of the front.



A method that utilizes Huygens construction on a spatial surface to equally distribute a set of points by distance on a pointy spatial surface is presented here. The proposed method keeps sharp features on a surface in three-dimensions and has 3^rd order accuracy where the surface is twice differentiable. The particle spacing can be modified to distribute the particles according to curvature (say) by using a curvature dependent speed of a curve with the Huygens construction.



The proposed method is employed in SDOT to track a 3D detonation front propagating is a homogeneous explosive while enforcing a boundary angle condition. Comparisons between SDOT tracking and exact solutions show the proposed resetting method is effective.