# Boundary SPH for Robust Particle-Mesh Interaction in Three Dimensions
## 4 Conclusions  
This paper describes a new approach of implementing the SPH boundary method. Our scheme, BSPH, takes advantage of 3D mesh architecture to create boundary manifolds that may be concave and feature complex geometry such as bowls or tunnels. The method is inspired by existing work in graphics and uses concepts from discrete signed distance fields, [PERSON]'s closest point querying algorithm, and [PERSON]'s methods for calculating normal vectors for faces, edges, and vertices. To evaluate and establish robustness for BSPH in application, we tested a variety of simulations in a _Unity3D_ implementation that utilizes compute shaders to optimize kernel neighborhood \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Scene** & **Num. Particles** &
\begin{tabular}{c} **Num.** \\ **Obstacles** \\ \end{tabular} & **Num. Vertices** & **Num. Edges** & **Num. Triangles** & **Average FPS** \\ \hline Flat Plane & 64 & 2 & 12 & 23 & 14 & 179.912 \\ \hline
10 Deg Inclined Plane (Slip) & 25 & 2 & 12 & 23 & 14 & 268.041 \\ \hline
10 Deg Inclined Plane (No-Slip) & 25 & 2 & 12 & 23 & 14 & 251.574 \\ \hline Tank (Empty) & 15,750 & 1 & 8 & 18 & 12 & 179.894 \\ \hline Tank (with Wedge) & 13,500 & 2 & 14 & 30 & 20 & 189.525 \\ \hline Dam Break & 20,445 & 2 & 14 & 30 & 20 & 149.303 \\ \hline Flow Field (Sphere) & 31,250 & 2 & 394 & 1170 & 780 & 155.875 \\ \hline Flow Field (Torus) & 31,250 & 2 & 392 & 1170 & 780 & 152.735 \\ \hline Flow Field (Bowl) & 31,250 & 2 & 144 & 408 & 272 & 150.070 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Mesh boundary performance by scene. calculations and parallelize particle operations. Our performance and empirical results show promise in BSPH's agility and ability to prevent submersion of particles into the boundary manifold, and we were successful in demonstrating that BSPH operates with similar effectiveness with both concave and convex mesh types. The average FPS performance indicates that BSPH can be run effectively over commonplace scenarios that are routine in computer graphics applications, for example in gaming and in special effects. We plan to further test the limitations of the mesh boundary method to identify how initial simulation parameters as well as the number of mesh vertices, edges, and triangles affect the runtime performance of the simulation. Our future efforts will also study whether edge cases can be identified through testing a more varied sample of mesh objects and whether the particle-mesh projection step can be further parallelized for additional flexibility in optimization. Furthermore, we will investigate the behavior of BSPH when integrated with double-precision values during mesh data pre-processing and during simulation. Finally, we aim to address the issue of irregular pressure values for particles close to the boundary in future iterations of the mesh boundary method. R.K.: Conceptualization, idea brainstorming, and formation; methodology, conceptualization, and mathematical formulation of the mesh boundary algorithm; software, implementation of the Unity3D build for prototyping, and result aggregation; writing--original draft preparation, submission drafting, and write-up; and literature review of existing boundary condition methods. P.M.T. : Supervision, project oversight, and guidance; project administration, providing the necessary computational hardware required to run SPH; and funding acquisition, aiding R.K. in achieving GAANN fellowship funding. All authors have read and agreed to the published version of the manuscript. [PERSON] was supported by a U.S. Department of Education Graduate Assistance in Areas of National Need (GAANN) fellowship under award P200A210096. The raw data supporting the conclusions of this article will be made available by the authors on request. The authors declare no conflicts of interest.