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Objectives
In this paper, we are going to talk about the radiation mode because one of the factors of modeling this equation is the view factor. So, radiative heat transfer or light transport are primarily governed by geometric view factors between surface elements. For general surfaces, calculating accurate geometric view factors requires solving integrals via quadrature methods. For complex scenes with many objects and obstacles such calculations are compute-intensive, preventing real-time simulations.
Vincent Vadez, François Brunetti, Pierre Alliez worked on a geometric and numerical to calculate the view factors between faces through a surface triangle mesh. In particular on a progressive approach which trades accuracy for time, primarily motivated by applications where time is critical. More specifically, a hybrid geometric/numerical method that performs an adaptive polygon-based quadrature is proposed. A hierarchical axis-aligned bounding box (AABB) tree data structure is used to accelerate obstacle detection, and a hierarchical forest data structure stores the input triangles that are recursively subdivided while the accuracy improves over time. Pairs of faces with either full or null mutual visibility are detected exactly by intersecting their 3D convex hull with the primitives of the AABB tree. These two cases lend to early terminations and closed form solutions. Faces with partial mutual visibility are adaptively subdivided using a SVM-based approach (support vector machine) such that the shadows cast by the obstacles (umbra or penumbra) are later best approximated by sums of closed form solutions. Such adaptive subdivision approach is combined with a prediction step utilizing point-based quadratures and segment shooting[ARTICLE].
So, the long-term objective is to reproduce the results presented in the article. However, the first objective is to replicate these results in feel++. Initially, we will achieve this by focusing on these smaller goals:
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We aim to deepen the understanding of radiative heat transfer mechanisms, with a particular emphasis on the importance of geometric view factors between surface elements
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Using the emission of rays tracing from one surface to receive them on another surface, along with the mechanisms and methods to create an algorithm capable of simulating this process
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Organization of geometric data using Bounding Volume Hierarchy (BVH) to accelerate ray tracing calculations: This method optimizes the search for intersection surfaces, thereby improving the efficiency and speed of ray tracing simulations.
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Compute view factors by applying the Monte Carlo ray tracing method. This approach aims to enhance the accuracy and efficiency of view factor calculations by leveraging probabilistic techniques to simulate complex geometries and interactions between surfaces
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computes view factors for planar faces in unobstructed radiative heat transfer scenarios using different numerical integration methods.