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Vector fields analysis traditionally distinguishes conservative (curl-free) from mass preserving (divergence-free) components. The Helmholtz-Hodge decomposition allows separating any vector field into the sum of three uniquely defined components: curl free, divergence free and harmonic. This decomposition is usually achieved by using mesh-based methods such as finite differences or finite elements...
In this paper, we present a new adaptive model for real-time fluid simulation with complex boundaries based on smoothed particle hydrodynamics (SPH) framework. Firstly, we introduce an adaptive SPH framework that is based on our character field function composed of 4 factors: geometrical complexity, boundary condition, physical complexity and complementary condition in terms of the neighboring particle...
The algorithm of the numerical decision of the hydrodynamics equations with representation of the decision on method of weighted residuals on the base of general neuronet's approximation in the whole flow area is developed. The algorithm is tested on decision of the two-dimensional Navier-Stokes equations.
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