Positivity-preserving discontinuous spectral element methods for compressible multi-species flows [PDF]
Computers & Fluids, 2023 We introduce a novel positivity-preserving, parameter-free numerical stabilisation approach for high-order discontinuous spectral element approximations of compressible multi-species flows.
W. Trojak, T. Dzanic
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Positivity-preserving schemes for some nonlinear stochastic PDEs [PDF]
arXiv.org, 2023 We introduce a positivity-preserving numerical scheme for a class of nonlinear stochastic heat equations driven by a purely time-dependent Brownian motion.
Charles-Edouard Br'ehier +2 more
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Positivity-preserving entropy filtering for the ideal magnetohydrodynamics equations [PDF]
Computers & Fluids, 2023 In this work, we present a positivity-preserving adaptive filtering approach for discontinuous spectral element approximations of the ideal magnetohydrodynamics equations.
T. Dzanic, F. Witherden
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THE SLICE BALANCE APPROACH USING AN ADAPTIVE-WEIGHTED CLOSURE [PDF]
EPJ Web of Conferences, 2021 In this paper, we present a formulation of the slice balance approach using a nonlinear closure relation derived analogously from the adaptive-weighted diamond-difference form of the weighted diamond-difference method for Cartesian grids.
Hackemack Michael W.
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A new Lagrange multiplier approach for constructing structure preserving schemes, I. Positivity preserving [PDF]
Computer Methods in Applied Mechanics and Engineering, 2021 We propose a new Lagrange multiplier approach to construct positivity preserving schemes for parabolic type equations. The new approach introduces a space-time Lagrange multiplier to enforce the positivity with the Karush-Kuhn-Tucker (KKT) conditions. We
Q. Cheng, Jie Shen
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Positivity-Preserving Entropy-Based Adaptive Filtering for Discontinuous Spectral Element Methods [PDF]
Journal of Computational Physics, 2022 In this work, we present a positivity-preserving entropy-based adaptive filtering method for shock capturing in discontinuous spectral element methods. By adapting the filter strength to enforce positivity and a local discrete minimum entropy principle ...
T. Dzanic, F. Witherden
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A general positivity-preserving algorithm for implicit high-order finite volume schemes solving the Euler and Navier-Stokes equations [PDF]
Journal of Computational Physics, 2023 This paper presents a general positivity-preserving algorithm for implicit high-order finite volume schemes solving Euler and Navier-Stokes equations.
Qian Huang, Yu-xin Ren, Qianqian Wang
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A positivity-preserving, energy stable scheme for a Ternary Cahn-Hilliard system with the singular interfacial parameters [PDF]
Journal of Computational Physics, 2021 In this paper, we construct and analyze a uniquely solvable, positivity preserving and unconditionally energy stable finite-difference scheme for the periodic three-component Macromolecular Microsphere Composite (MMC) hydrogels system, a ternary Cahn ...
Lixiu Dong +3 more
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A positivity preserving strategy for entropy stable discontinuous Galerkin discretizations of the compressible Euler and Navier-Stokes equations [PDF]
Journal of Computational Physics, 2022 High-order entropy-stable discontinuous Galerkin methods for the compressible Euler and Navier-Stokes equations require the positivity of thermodynamic quantities in order to guarantee their well-posedness.
Yimin Lin, Jesse Chan, I. Tomas
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Preserving Positive Intermediate Curvature
The Journal of Geometric Analysis, 2023 AbstractConsider a compact manifoldN(with or without boundary) of dimensionn. Positivem-intermediate curvature interpolates between positive Ricci curvature ($$m = 1$$m=1) and positive scalar curvature ($$m = n-1$$m=n-1), and it is obstructed on partial tori$$N^n = M^{n-m} \times \mathbb {T}^m$$Nn=Mn-m×Tm. Given Riemannian metrics$$g, {\bar{g}}$$g,g¯on$
Tsz-Kiu Aaron Chow +2 more
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