Article
Computer Science, Interdisciplinary Applications
Remi Bourgeois, Dongwook Lee
Summary: We present GPMOOD, an a posteriori shock-capturing finite volume method algorithm that solves a compressible hyperbolic conservative system with high-order solution accuracy in multiple spatial dimensions. This method combines the spatial reconstruction methods of Gaussian Process (GP) with the detection algorithms of Multidimensional Optimal Order Detection (MOOD), allowing for flexible variability of spatial accuracy.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics, Applied
Raphael Louberea, Rodolphe Turpault, Alexandre Bourriaud
Summary: In this paper, a novel Finite Volume (FV) scheme is proposed for high-order approximations of multi-dimensional hyperbolic systems of conservation laws within an Adaptive Mesh Refinement framework. The scheme utilizes a point-wise polynomial reconstruction method that avoids recalculating reconstruction stencils and matrices during mesh refinement or coarsening. It also integrates the limiting of the FV scheme and the refinement procedure using the Multi-dimensional Optimal Order Detection (MOOD) criteria. The efficiency of the proposed computational procedure is demonstrated through simulations of increasingly challenging test cases using the Euler system and the radiative M 1 model.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Computer Science, Interdisciplinary Applications
Chuan Fan, Xiangxiong Zhang, Jianxian Qiu
Summary: This paper introduces a positivity-preserving hybrid HWENO scheme for compressible Navier-Stokes equations, which is more efficient and robust than the conventional HWENO method, especially suitable for solving gas dynamics equations in low density and low pressure conditions.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Physics, Multidisciplinary
Di Yang, Gang Peng, Zhiming Gao
Summary: This paper proposes a positivity-preserving finite volume scheme for simulating the nonequilibrium radiation diffusion equations on distorted meshes. The scheme uses fixed stencils and is locally conservative. It utilizes an interpolation algorithm to calculate auxiliary unknowns, while the primary unknowns are cell-centered. The scheme is shown to be efficient and strong in preserving positivity through numerical results.
Article
Computer Science, Interdisciplinary Applications
Antoine Laurain, Shawn W. Walker
Summary: This study develops a framework and numerical method for controlling the full space-time tube of a geometrically driven flow. By minimizing an appropriate cost functional, the control of the trajectory of the flow is achieved, demonstrating the efficiency of the approach in two and three dimensions.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics, Applied
S. Mousavi Yeganeh, J. Farzi
Summary: This paper utilizes MPP and PP parametrized flux limiters to achieve strict maximum principle and positivity-preserving property for solving hyperbolic conservation laws, demonstrating efficiency and effectiveness through high-order MPP RK-SV and PP RK-SV schemes. The proposed schemes maintain the maximum principle without additional time step restrictions and preserve the high-order accuracy for linear advection problems.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Gang Peng, Zhiming Gao, Wenjing Yan, Xinlong Feng
Summary: This paper introduces a new cell-centered positivity-preserving finite volume scheme for solving 3D anisotropic diffusion problems on distorted meshes. The scheme utilizes primary and auxiliary unknowns, with discretization, interpolation, and acceleration methods to improve computational efficiency and numerical accuracy.
COMPUTER PHYSICS COMMUNICATIONS
(2021)
Article
Computer Science, Interdisciplinary Applications
Jaeyoung Jung, Jin Hwan Hwang
Summary: The present study developed a path-conservative high-order positivity-preserving well-balanced finite volume Riemann solver for the one-dimensional porous shallow water equations with discontinuous porosity and bottom topography. The study formulated finite difference equations using the path-conservative approach and implemented the weighted essentially non-oscillatory (WENO) and the Runge-Kutta methods for spatiotemporal discretization. The model exhibited positivity-preserving and well-balanced properties with high-order accuracy and the ability to capture shocks.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Applied
Jinjing Xu, Fei Zhao, Zhiqiang Sheng, Guangwei Yuan
Summary: In this paper, the neutron diffusion kinetics equation with delayed neutrons is studied. A positivity theorem is proposed, and a nonlinear positivity-preserving finite volume scheme is developed to deal with discontinuous and anisotropy diffusion coefficient problems. The existence of solution for the nonlinear system is proved under certain constraint on time step size. Three nonlinear iteration strategies are introduced to solve the system. Numerical experiments demonstrate the scheme's positivity-preserving property and second order accuracy in space. The computational costs of the iteration strategies are compared, and a necessary constraint on time step size for convergence is shown with another example.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Computer Science, Interdisciplinary Applications
T. Dzanic, F. D. Witherden
Summary: This work presents a positivity-preserving entropy-based adaptive filtering method for shock capturing in discontinuous spectral element methods. The method adapts the filter strength to enforce positivity and a local discrete minimum entropy principle, allowing it to robustly handle strong discontinuities with sub-element resolution. It does not require problem-dependent parameter tuning and can be easily implemented on general unstructured meshes with relatively low computational cost.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics, Applied
Gang Peng
Summary: A new positivity-preserving finite volume scheme is proposed for solving the convection-diffusion equation on distorted meshes in 2D or 3D. The scheme utilizes a nonlinear two-point flux approximation for diffusion flux and a second-order upwind method with a slope limiter for convection flux. The scheme exhibits second-order convergence rate and is effective in solving the convection-diffusion problem based on numerical results.
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Mengqing Liu, Man Zhang, Caixia Li, Fang Shen
Summary: This paper introduces a modified reconstruction method that preserves the conservation of cell average values and combines the divergence-free constraint with conservative features to make the magnetic field locally divergence-free. The proposed scheme maintains both the divergence-free constraint and ENO property for the magnetic field without using any limiter, and is applicable to simulations of ideal MHD equations.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Ziyao Xu, Chi -Wang Shu
Summary: This study is a follow-up work that improves and extends the positivity-preserving discontinuous Galerkin methods for stationary hyperbolic equations. Previous methods were only applicable to equations with constant coefficients and achieved second order accuracy. In this study, we propose high order positivity-preserving DG methods for one-dimensional variable coefficient and nonlinear equations, as well as two and three-dimensional stationary hyperbolic equations with constant coefficients. The algorithms are validated through extensive numerical experiments.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Physics, Mathematical
Shuai Su, Huazhong Tang, Jiming Wu
Summary: This paper introduces an efficient finite volume scheme on general polygonal meshes for calculating the two-dimensional nonequilibrium three-temperature radiation diffusion equations. The scheme does not require nonlinear iteration for linear problems and can ensure the positivity, existence, and uniqueness of the cell-centered solutions obtained on the corrector phase. Numerical experiments demonstrate the accuracy, efficiency, and positivity of the scheme on various distorted meshes.
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
(2021)
Article
Mathematical & Computational Biology
Lin Zhang, Yongbin Ge, Xiaojia Yang
Summary: The Keller-Segel model is a crucial tool for simulating biological processes, consisting of a reaction-diffusion-chemotaxis equation and a reaction-diffusion equation. However, most numerical methods used to solve this model lack accuracy in the temporal direction. Therefore, a high-precision and stable compact difference scheme is proposed in this study, which employs a fourth-order backward difference formula and compact difference operators for discretization. The proposed method is verified through numerical experiments, including finite-time blow-up, non-negativity, mass conservation, and energy dissipation.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2023)
Article
Energy & Fuels
Andres A. Salazar, Yuzhang Che, Jiafeng Zheng, Feng Xiao
Summary: This study introduces a novel error correction method using a multivariable neural network in short-term, hub-height wind speed forecasting systems, showing its effectiveness and advantages in complex wind pattern regions.
ENERGY SCIENCE & ENGINEERING
(2022)
Article
Meteorology & Atmospheric Sciences
Pei Huang, Chungang Chen, Xingliang Li, Xueshun Shen, Feng Xiao
Summary: An adaptive 2D nonhydrostatic dynamical core is proposed using the MCV scheme and the Berger-Oliger AMR algorithm. The introduced constraints ensure conservation while maintaining flexibility. Numerical experiments demonstrate that the adaptive model improves computational efficiency without sacrificing accuracy.
ADVANCES IN ATMOSPHERIC SCIENCES
(2022)
Article
Computer Science, Interdisciplinary Applications
Hiro Wakimura, Shinichi Takagi, Feng Xiao
Summary: A class of high-order shock-capturing schemes, PnTm-BVD, has been developed to solve Euler equations with reduced numerical dissipation. This study thoroughly examines the mechanisms of symmetry-breaking in a finite volume framework with the P4T2-BVD reconstruction scheme and proposes modifications to completely remove the causes for symmetry breaking. Benchmark tests confirm perfect symmetric solution structures.
COMPUTERS & FLUIDS
(2022)
Article
Computer Science, Interdisciplinary Applications
Dezhu Chen, Bin Xie, Feng Xiao
Summary: This article revisits the THINC/QQ scheme and investigates its numerical properties. It also presents recent progress made on the algorithm to improve accuracy and robustness. Verification tests on different types of grids demonstrate that the improved THINC/QQ scheme delivers higher accuracy and robustness, and effectively competes with other existing interface capturing methods.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2022)
Article
Mechanics
Teng Xiao, Bin Xie, Xi Deng, Yanping Du
Summary: In this work, high-fidelity numerical solvers for turbulent cavitation flows were developed and used to simulate cavitation and supercavitation. The proposed solver utilizes the VOF function, interface capture method, and mass transfer models to accurately resolve cavitation bubble structures. The simulations show better agreement with experimental data and theoretical solutions compared to previous works, validating the high-fidelity predictions of the proposed solver for turbulent cavitation simulations.
Article
Energy & Fuels
Andres A. Salazar, Jiafeng Zheng, Yuzhang Che, Feng Xiao
Summary: This work introduces a novel method to generate probabilistic hub-height wind speed forecasts. By employing state-of-the-art convolutional variational autoencoders trained with historical wind speed observations and outputs from a numerical weather prediction model, accurate wind speed forecasts can be achieved. The proposed method also performs well in challenging areas with complex topography and highly fluctuating wind patterns.
ENERGY SCIENCE & ENGINEERING
(2022)
Article
Computer Science, Interdisciplinary Applications
Bin Xie, Xi Deng, Feng Xiao
Summary: This paper proposes a novel high-order finite volume scheme for arbitrary unstructured grids. The scheme uses a multi-stage reconstruction procedure with a compact stencil to determine the coefficients of the reconstruction polynomial. The proposed method, FVMS4, improves solution accuracy without extending the reconstruction stencil, making it algorithmically simple and numerically efficient. By combining it with a limiting projection scheme, AOD, the method can handle smooth and discontinuous solutions, providing essentially non-oscillatory, less-dissipative and highly accurate results.
COMPUTERS & FLUIDS
(2022)
Article
Computer Science, Interdisciplinary Applications
Xi Deng, Zhen-hua Jiang, Peter Vincent, Feng Xiao, Chao Yan
Summary: This study proposes a new dissipation-adjustable shock-capturing scheme for resolving multi-scale flow structures in high speed compressible flow. The scheme has the advantages of capturing large-scale discontinuous structures, adjustable numerical dissipation property, and suitability for solving small-scale structures.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Peng Jin, Ahmed Al-Rikabi, Xi Deng
Summary: In this work, a new family of WENO schemes based on a three-cell stencil is designed to address the scale-invariant property and accuracy issues in existing WENO schemes. The new WENO weighting functions, which depend on cell Normalised Volume Integrated Average (NVIA) values and a shape parameter, are designed to achieve scale-invariant property. By introducing an additional ENO constraint, the maximum value of the shape parameter that corresponds to optimal accuracy can be determined. Accuracy analysis and benchmark tests show that the proposed weighting functions outperform existing three-cell-based WENO schemes. Therefore, this work proposes a new direction for constructing scale-invariant WENO weighting functions with optimal accuracy.
COMPUTERS & FLUIDS
(2023)
Article
Computer Science, Interdisciplinary Applications
Xi Deng
Summary: This article introduces the discretization of the convection term in a three-cell compact stencil, which is widely used in engineering Computational Fluid Dynamics. The author proposes a Unified Normalisedvariable Diagram (UND) framework and a new reconstruction scheme named ROUND based on UND. The ROUND scheme shows superior performance in accuracy and resolution.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mechanics
Jian Fang, Xi Deng, Zhi X. Chen
Summary: A Mach 1.5 non-reactive flow in a cavity-stabilized combustor of a model scramjet was studied via direct-numerical simulation, with focus on the interaction among boundary layer, free shear-layer above the cavity and shock wave. Impingement of the free shear-layer on the aft wall of the cavity leads to strong turbulence, high pressure, and compression waves. The analysis reveals that shear production amplifies turbulence in the core of the shear-layer, while deceleration production has a significant impact above the aft wall of the cavity and around the shock interaction points.
Article
Nanoscience & Nanotechnology
Xi Deng, James C. Massey, Nedunchezhian Swaminathan
Summary: In this study, a low-dissipative, structure-preserving ROUND scheme is tested for LES of reacting flows. The scheme demonstrates high efficiency, accuracy, and structure-preserving property, improving the numerical resolution and prediction of flow statistics, and preserving the axisymmetry of the flow. The ROUND scheme avoids nonphysical numerical oscillations and compares well with measurements.
Article
Engineering, Aerospace
Lidong Cheng, Xi Deng, Bin Xie
Summary: This study proposes a practical numerical solver for simulations of shock-vortex and shock-turbulence problems in high-speed flows. The solver can simultaneously handle large-scale flow structures, resolvable flow structures, and under-resolve isotropic sub-grid scales. It has been verified through experiments and comparisons, and provides an accurate and practical numerical solver for these problems.
Article
Mechanics
Y. Xiong, B. Xie, F. Xiao
Summary: In this paper, a concise and efficient interface capturing scheme for incompressible fluid simulation with surface tension on polyhedral unstructured mesh is presented. The scheme combines the positive aspects of the VOF method and the level-set method, and has been validated to be accurate and efficient compared with other advanced methods.
Article
Computer Science, Interdisciplinary Applications
Xi Deng
Summary: This work develops a new finite volume convection scheme and open-source library for convection-dominated problems on unstructured grids. The scheme achieves high resolution and structure-preservation by adjusting numerical dissipation and anti-dissipation errors. The performance of the scheme is verified through accuracy tests and it shows significant reduction in numerical errors and improved structure-preservation.
JOURNAL OF COMPUTATIONAL SCIENCE
(2023)
Article
Computer Science, Interdisciplinary Applications
Ashish Bhole, Herve Guillard, Boniface Nkonga, Francesca Rapetti
Summary: Finite elements of class C-1 are used for computing magnetohydrodynamics instabilities in tokamak plasmas, and isoparametric approximations are employed to align the mesh with the magnetic field line. This numerical framework helps in understanding the operation of existing devices and predicting optimal strategies for the international ITER tokamak. However, a mesh-aligned isoparametric representation encounters issues near critical points of the magnetic field, which can be addressed by combining aligned and unaligned meshes.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2024)
Article
Computer Science, Interdisciplinary Applications
Federico Vismara, Tommaso Benacchio
Summary: This paper introduces a method for solving hyperbolic-parabolic problems on multidimensional semi-infinite domains. By dividing the computational domain into bounded and unbounded subdomains and coupling them using numerical fluxes at the interface, accurate numerical solutions are obtained. In addition, computational cost can be reduced by tuning the parameters of the basis functions.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2024)
Article
Computer Science, Interdisciplinary Applications
Keigo Enomoto, Takato Ishida, Yuya Doi, Takashi Uneyama, Yuichi Masubuchi
Summary: We have developed a novel Moving Particle Simulation (MPS) method to accurately reproduce the motion of fibers in sheared liquids. By introducing the micropolar fluid model, we address the issue of fibers being aligned with the flow direction in conventional MPS simulations. Our method is capable of accurately reproducing the fiber motion predicted by Jeffery's theory.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2024)