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  1. Efficiently and accurately simulating partial differential equations(PDEs) in and around arbitrarily defined geometries, especially with high levels of adaptivity, has significant implications for different application domains. A key bottleneck in the above process is the fast construction of a "good" adaptively-refined mesh. In this work, we present an efficient novel octree-based adaptive discretization approach capable of caring out arbitrarily shaped void regions from the parent domain: an essential requirement for fluid simulations around complex objects.