Article
Computer Science, Interdisciplinary Applications
Magnus Svard
Summary: This study focuses on deriving boundary conditions for the initial-boundary value Euler equations to establish an entropy bound for the physical (Navier-Stokes) entropy. The research begins by reviewing the entropy bound obtained for standard no-penetration wall boundary conditions and proposes a numerical implementation. The main results include deriving full-state boundary conditions and demonstrating that linear theory boundary conditions are unable to bound the entropy, requiring nonlinear bounds and additional boundary conditions. The theoretical findings are supported by numerical experiments.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Marian G. S. Izsak, Hans -Jakob Kaltenbach
Summary: This paper develops a Cartesian cut-cell method for solving the linearized Euler equations and incorporates additional boundary constraints into the Hermite-based finite-difference stencil near the boundary. The proposed method improves the accuracy and stability of the numerical scheme for both 1D and multidimensional cases. The numerical experiments demonstrate the effectiveness of the proposed method in improving the modified wavenumber signature of the boundary stencils. Rating: 8 out of 10.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Applied
Gustav Eriksson, Ken Mattsson
Summary: This paper presents the solution of the pressure-velocity formulation of the incompressible Navier-Stokes equations using high-order finite difference operators. Two methods for imposing Dirichlet boundary conditions are introduced and proven to be stable. The accuracy and convergence of the methods are verified through theoretical analysis and numerical experiments.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Engineering, Multidisciplinary
Chuan Fan, Zhuang Zhao, Tao Xiong, Jianxian Qiu
Summary: In this paper, a robust fifth order finite difference Hermite weighted essentially non-oscillatory (HWENO) scheme for compressible Euler equations is proposed. The proposed scheme performs flux reconstructions in the finite difference framework without using the derivative value of a target cell, resulting in a simpler and more robust scheme.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Mathematics, Applied
Hongwei Li
Summary: This paper focuses on designing and analyzing local absorbing boundary conditions for the nonlinear Schrodinger equation with wave operator on unbounded domains in two dimensions. The proposed method is effective and feasible, as demonstrated by numerical results.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics
Zhizhuang Zhang, Xiangyu Zhou, Gang Li, Shouguo Qian, Qiang Niu
Summary: This paper introduces a method to construct an entropy stable finite difference scheme for nonlinear hyperbolic systems of conservation laws. The method can maintain the discrete entropy inequality and achieve high-order accuracy. Firstly, a second-order accurate semi-discrete entropy conservative scheme is constructed. Then, this scheme is used as a building block to achieve high-order accurate semi-discrete entropy conservative schemes. Finally, a dissipation term based on the Weighted Essentially Non-Oscillatory (WENO) reconstruction is added to obtain the high-order entropy stable schemes, which are integrated in time using the third-order Runge-Kutta (RK) approach.
Article
Mechanics
Jun Nagao, Abhishek Lakshman Pillai, Takeshi Shoji, Shigeru Tachibana, Takeshi Yokomori, Ryoichi Kurose
Summary: A hybrid computational fluid dynamics (CFD)/computational aero-acoustics (CAA) approach, namely the hybrid LES/APE-RF approach, is used to analyze the impact of a wall on the combustion noise from a low-swirl turbulent jet flame. The results show that the SPL spectrum obtained from the LES/APE-RF is in good agreement with the experimental measurements. The presence of the wall plate alters the flame fluctuation phenomena by creating an asymmetric flow around the flame and distorting the flame structure.
Article
Computer Science, Interdisciplinary Applications
K. R. Arun, Asha K. Dond, Rakesh Kumar
Summary: This article proposes a new troubled-cell indicator utilizing the smoothness indicators of WENO schemes for hyperbolic conservation laws. Three new adaptive WENO algorithms of high-order accuracy are constructed based on the proposed indicator. The algorithms are efficient and take 30%-75% less computational time than the WENO-Z schemes while retaining the advantages of WENO-Z schemes.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2023)
Article
Computer Science, Interdisciplinary Applications
Jan Nordstrom, Andrew R. Winters
Summary: Boundary conditions and estimates for systems of the nonlinear shallow water equations in two spatial dimensions are derived based on energy and entropy analysis. It is found that the energy method provides more detailed information and is consistent with the entropy analysis. The nonlinear energy analysis reveals the differences between linear and nonlinear analysis and shows that the results from linear analysis may not hold in the nonlinear case. The nonlinear analysis generally requires a different minimal number of boundary conditions compared to the linear analysis, and the magnitude of the flow does not influence the number of required boundary conditions.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Construction & Building Technology
Francesco Nicoletti, Mario Antonio Cucumo, Natale Arcuri
Summary: This paper aims to compare the accuracy and test duration of different methods for in-situ measurement of wall thermal conductance. The study reveals that the commonly used method (HFM) yields high errors when the heat flow meter is on the surface opposite the insulation. The dynamic method described in the UNI ISO 9869-1 standard is inadequate for abrupt temperature changes.
ENERGY AND BUILDINGS
(2023)
Article
Engineering, Aerospace
Z. J. Wang
Summary: In this study, an algebraic equilibrium wall model previously developed for hexahedral elements is extended to handle mixed meshes including prismatic, tetrahedral, and pyramidal elements in a discontinuous high-order method. The extension is necessary for complex geometries where high-order mixed elements are needed near solid walls. Various design decisions are discussed to optimize the performance of a production-level high-order large-eddy simulation solver on massively parallel CPU/GPU architectures. The extended model is evaluated using benchmark problems and compared with experimental data on flow over a high-lift model.
Article
Mathematics, Applied
Xuan-ru Lu, Guang-Hua Gao, Zhi-Zhong Sun
Summary: This paper studies the fourth-order parabolic equations with different boundary value conditions and proposes corresponding difference schemes and interpolation formulas. The convergence, stability, and uniqueness of the numerical solutions are proved, and the results are validated through numerical experiments.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Computer Science, Interdisciplinary Applications
Remi Abgrall, Philipp Oeffner, Hendrik Ranocha
Summary: This paper proposes an approach to construct entropy conservative/dissipative semidiscretizations in the general class of residual distribution (RD) schemes. The approach involves adding suitable correction terms characterized as solutions of certain optimization problems. The method is applied to the SBP- SAT framework and novel generalizations to entropy inequalities, multiple constraints, and kinetic energy preservation for the Euler equations are developed. Explicit solutions are provided for all optimization problems, and a fully discrete entropy conservative/dissipative RD scheme is obtained using the deferred correction method for time integration.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics, Applied
Hristo Kojouharov, Souvik Roy, Madhu Gupta, Fawaz Alalhareth, John M. Slezak
Summary: A new modified nonstandard finite difference method is developed for solving one-dimensional autonomous differential equations, based on the theta method with elementary stability and second-order accuracy. Numerical simulations are presented to validate the theoretical results.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Computer Science, Interdisciplinary Applications
Deepak Bhoriya, Harish Kumar, Praveen Chandrashekar
Summary: In this article, high-order finite-difference entropy stable schemes are proposed for the two-fluid relativistic plasma flow equations. The schemes are designed by exploiting the structure of the equations, which consist of three independent flux components. The coupling of ion and electron flows and electromagnetic fields is achieved through source terms, without affecting the entropy evolution. The proposed schemes are tested and demonstrated to be stable, accurate, and efficient using various test problems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
