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Established in 2020, POSTECH Mathematical Institute for Data Science (MINDS) is the community of researchers in the areas of fundamental data science, machine learning, artificial intelligence, scientific computing, and humanitarian data science. MINDS mission is to provide a platform for collaboration among researchers and to provide various opportunities for students in data science. MINDS also aims to use our data science research to serve our local and global communities pursuing humanitarian data science.


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MINDS Seminar Series | Wai-Sun Don (Ocean University of China) - Affine-invariant WENO weights and their applications in solving hyperbolic conservation laws

period : 2023-04-27 ~ 2023-04-27
time : 17:00:00 ~ 18:00
개최 장소 : Math Bldg & Online streaming (Zoom)
Topic : Affine-invariant WENO weights and their applications in solving hyperbolic conservation laws
Date 2023-04-27 ~ 2023-04-27 Time 17:00:00 ~ 18:00
Speaker Wai-Sun Don Affiliation Ocean University of China
Place Math Bldg & Online streaming (Zoom) Streaming link ID : 688 896 1076 / PW : 54321
Topic Affine-invariant WENO weights and their applications in solving hyperbolic conservation laws
Contents The user-defined sensitivity parameter responsible for avoiding zero division in the WENO nonlinear weights had plagued the schemes' performance in resolving smooth function with high-order critical points (CP-property) and capturing discontinuity essentially non-oscillatory (ENO-property). In this talk, a novel and simple yet effective WENO weights (Ai-weights) is devised for the (affine-invariant) Ai-WENO operator to handle the case when the function being reconstructed undergoes an affine transformation (Ai-operator) with a constant scaling and translation (Ai-coefficients) within a global stencil. The Ai-weights essentially decouple the inter-dependencies of the Ai-coefficients and sensitivity parameter effectively. For any given sensitivity parameter, the Ai-WENO operator guarantees that the WENO operator and the affine-transformation operator are commutable, as proven theoretically and validated numerically. In the presence of discontinuities, the high-order characteristic-wise (Ai-)(A-) WENO-Z finite difference scheme satisfies the ENO-property even when the classical WENO-JS and WENO-Z schemes might not. Examples in the shallow water wave equations, the Euler equations under gravitational fields solved by the characteristic-wise Ai-WENO scheme, are intrinsically well-balanced (WB-property). The two-medium γ-based model of the stiffened gas is also solved by the Ai-WENO operator, which preserves the equilibriums of velocity and pressure around the medium interface. A hybrid flux-based bound- and positivity-preserving (BP-P) limiter is also implemented to enforce the physical constraints. The theoretical analysis yields the exact CFL condition, which depends nonlinearly on the local Mach number. A variety of one-, two-, and three-dimensional benchmark two-medium shock-tube problems illustrate the high-order accuracy and enhanced robustness. In summary, any Ai-weights-based WENO reconstruction/interpolation operator enhances the robustness and reliability of the WENO scheme for solving hyperbolic conservation laws.
MinDS MinDS · 2023-03-06 16:27 · Views 643

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