Article
Computer Science, Interdisciplinary Applications
Kleiton A. Schneider, Jose M. Gallardo, Dinshaw S. Balsara, Boniface Nkonga, Carlos Pares
Summary: This paper discusses the development of efficient incomplete multidimensional Riemann solvers for hyperbolic systems, presents a general strategy for constructing these solvers, and demonstrates the advantages of AVM schemes. Numerical experiments are conducted to test the performance of the proposed schemes.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Carlos Pares, Carlos Pares-Pulido
Summary: This paper presents high order well-balanced finite difference weighted essentially non-oscillatory methods for solving general systems of balance laws. Two different families of methods are introduced, discussing their properties and applications in systems with singular source terms. The methods are applied to derive third and fifth order well-balanced methods for various equations, including the shallow water model.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics
Ernesto Guerrero Fernandez, Cipriano Escalante, Manuel J. Castro Diaz
Summary: This work introduces a general strategy for developing high-order DG numerical schemes for systems of balance laws. The strategy ensures the well-balanced character of the resulting numerical method for smooth stationary solutions through a local projection step. The method can be adapted to different time marching DG discretisations and includes a limiting procedure based on a modified WENO approach to handle spurious oscillations caused by non-smooth solutions while preserving the well-balanced properties of the scheme.
Article
Mathematics
Irene Gomez-Bueno, Manuel Jesus Castro Diaz, Carlos Pares, Giovanni Russo
Summary: The authors introduced a new technique to design high-order numerical methods for balance laws by using collocation RK methods to solve local non-linear problems. They also presented a well-balanced reconstruction operator in previous works to preserve all stationary solutions. The efficiency of the methods was tested on a variety of tests, from simple academic systems to more complex equations with gravity effects.
Article
Computer Science, Interdisciplinary Applications
Mokbel Karam, Tony Saad
Summary: A new framework is proposed for designing fast-projection solvers for the Navier-Stokes equations using Runge-Kutta integrators, which involves tracking nonlinear advection terms and replacing pressure projection with suitable approximations. The proposed pseudo-pressure approximations are easy to implement and can be optimized for stability or other desirable properties. Additionally, approximations for adaptive timestepping are reported for the first time, verifying the correctness and accuracy of the results.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Applied
Irene Gomez-Bueno, Manuel J. Castro, Carlos Pares
Summary: The study presents a strategy to develop high-order numerical methods for systems of balance laws, focusing on a well-balanced reconstruction operator. It introduces a technique to modify standard reconstruction operators and has been successfully applied to various systems of balance laws. The approach involves solving nonlinear problems in a control problem format to achieve well-balancedness.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Mathematics, Applied
Nguyen Xuan Thanh, Mai Duc Thanh, Dao Huy Cuong
Summary: A well-balanced high-order scheme for shallow water equations with variable topography and temperature gradient is developed, showing excellent accuracy in capturing smooth solutions and elementary discontinuities. Numerical tests demonstrate its superiority over the Godunov-type scheme, even in the resonant regime. Wave interaction problems also exhibit good accuracy, with the superbee limiter found to provide more accurate approximations than Van Leer's limiter.
ADVANCES IN COMPUTATIONAL MATHEMATICS
(2021)
Article
Mathematics, Applied
Christophe Berthon, Solene Bulteau, Francoise Foucher, Meissa M'Baye, Victor Michel-Dansac
Summary: This study proposes a simple correction method that improves the preservation of steady states in high-order finite volume schemes when approximating weak solutions of hyperbolic systems. Compared to traditional techniques, this method avoids the inversion of nonlinear functions and is able to handle underdetermined stationary systems.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2022)
Article
Computer Science, Interdisciplinary Applications
Yaguang Gu, Zhen Gao, Guanghui Hu, Peng Li, Qingcheng Fu
Summary: In this paper, a fifth order well-balanced positivity-preserving finite difference scale-invariant AWENO scheme is proposed for the compressible Euler equations. The scheme is designed to ensure well-balancedness and positivity of the density and pressure throughout the computation. The use of the Si-WENO operator and interpolation-based and flux-based positivity-preserving limiters improve computational efficiency.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Chemistry, Multidisciplinary
SeyedBijan Mahbaz, Ali Yaghoubi, Alireza Dehghani-Sanij, Erfan Sarvaramini, Yuri Leonenko, Maurice B. Dusseault
Summary: Renewable and sustainable energy sources, such as geothermal well-doublet systems, can contribute to meeting global energy needs and addressing environmental challenges. However, challenges related to heat transfer, chemical processes, and mechanical issues need to be carefully examined and optimized to ensure cost-effectiveness and reduced risks in the operation of such systems.
APPLIED SCIENCES-BASEL
(2021)
Article
Mathematics, Applied
Kleiton A. Schneider, Jose M. Gallardo, Cipriano Escalante
Summary: This paper presents an efficient and genuinely two-dimensional Riemann solver for hyperbolic nonconservative systems. The solver only requires a bound on the maximal propagation speeds in the coordinate directions and the amount of numerical diffusion can be controlled easily. Special attention is given to its applications in shallow water systems with topography and dry areas. The paper describes an extension of the numerical schemes for correctly handling wet-dry transitions in the computational domain and proposes an efficient implementation of the schemes using GPUs. Numerical experiments show that the schemes are generally more efficient than their 1d x 1d counterparts.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Computer Science, Artificial Intelligence
Min Shi, Jialin Shen, Qingming Yi, Jian Weng, Zunkai Huang, Aiwen Luo, Yicong Zhou
Summary: This article introduces a lightweight multiscale-feature-fusion network (LMFFNet) that achieves a good balance between accuracy and inference speed in real-time semantic segmentation. The network extracts features with fewer parameters, fuses multiscale semantic features to improve segmentation accuracy, and recovers details of input images through the attention mechanism. Experiments demonstrate that the proposed network is suitable for autonomous driving and robotics.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2023)
Article
Mechanics
Zhaoli Guo
Summary: By analyzing the discrete balance equation of LBE, researchers proposed a well-balanced LBE model that can achieve discrete equilibrium state. The well-balance properties of the model have been confirmed through simulations.
Article
Computer Science, Interdisciplinary Applications
Jonas P. Berberich, Praveen Chandrashekar, Christian Klingenberg
Summary: The study introduces a general framework for constructing well-balanced finite volume methods for hyperbolic balance laws. The proposed method can be applied to follow any solution of any system of hyperbolic balance laws in multiple spatial dimensions. By modifying the standard finite volume approach, the well-balancing property is achieved and maintained even with high order accuracy.
COMPUTERS & FLUIDS
(2021)
Article
Physics, Mathematical
Jonas P. Berberich, Roger Kaeppeli, Praveen Chandrashekar, Christian Klingenberg
Summary: The study introduces novel high order well-balanced finite volume methods for the full compressible Euler system with gravity source term. These methods are simple, flexible, and robust, and not limited to a specific equation of state. Numerical tests show that they improve the capability to accurately resolve small perturbations on hydrostatic states.
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
(2021)