Article
Mathematics, Applied
Buyang Li, Weifeng Qiu, Zongze Yang
Summary: We propose a linearized semi-implicit and decoupled finite element method for the incompressible Navier-Stokes equations with variable density. The method solves the velocity equation using an H-1-conforming finite element method and the density equation using an upwind discontinuous Galerkin finite element method with post-processed velocity. The proposed method is proven to converge in approximating reasonably smooth solutions in three-dimensional convex polyhedral domains.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Computer Science, Interdisciplinary Applications
Niklas Fehn, Johannes Heinz, Wolfgang A. Wall, Martin Kronbichler
Summary: This paper presents robust discontinuous Galerkin methods for the incompressible Navier-Stokes equations on moving meshes. It introduces high-order accurate arbitrary Lagrangian-Eulerian formulations in a unified framework for various types of Navier-Stokes solvers. Numerical validations demonstrate that the proposed formulations maintain the formal order of accuracy of the Navier-Stokes solvers in both space and time.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Engineering, Multidisciplinary
Fan Zhang, Tiegang Liu, Moubin Liu
Summary: This paper presents a third-order reconstructed discontinuous Galerkin (DG) method based on a weighted variational minimization principle for solving incompressible flow problems on unstructured grids. The method achieves optimal third-order accuracy at reduced computational costs and outperforms reconstructed DG methods based on least-squares or Green-Gauss reconstruction for simulating incompressible flows.
APPLIED MATHEMATICAL MODELLING
(2021)
Article
Mathematics, Applied
Keegan L. A. Kirk, Aycil Cesmelioglu, Sander Rhebergen
Summary: This article proves the convergence of a space-time hybridized discontinuous Galerkin method for the evolutionary Navier-Stokes equations as the time step and mesh size approach zero, and further demonstrates that the weak solution satisfies the energy inequality. The analysis is carried out using discrete functional analysis tools and a discrete version of the Aubin-Lions-Simon theorem.
MATHEMATICS OF COMPUTATION
(2022)
Article
Mathematics, Applied
Yongbin Han, Yanren Hou
Summary: In this paper, an embedded-hybridized discontinuous Galerkin method for the time-dependent Navier-Stokes equations is proposed, and a prior error estimate is presented. The error estimates include the velocity error in the L-2(Omega) norm and a Reynolds-dependent error bound.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Mathematics, Applied
Mofdi El-Amrani, Abdelouahed Ouardghi, Mohammed Seaid
Summary: An adaptive enriched Galerkin-characteristics finite element method is proposed for efficient numerical solution of incompressible Navier-Stokes equations, combining various techniques for improved efficiency and accuracy. The method adapts enrichments based on the gradient of the velocity field as an error indicator and is capable of resolving complex flow features in irregular geometries.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2021)
Article
Mathematics, Applied
Zhaonan Dong, Emmanuil H. Georgoulis
Summary: A new variant of the IPDG method, called robust IPDG (RIPDG), is proposed, which involves weighted averages of the gradient of the approximate solution to enhance its robustness. Numerical experiments show that the RIPDG method performs better than the standard IPDG method in terms of error behavior and conditioning in scenarios with strong local variation.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Qiaolin He, Xiaoding Shi
Summary: This paper introduces a fully discrete method combining LDG finite element method and SAV approach for the compressible Navier-Stokes-Allen-Cahn system, allowing separate solution of velocity, density, and mass concentration of fluid mixture, and using SDC method to improve temporal accuracy. Numerical experiments demonstrate the high accuracy in both time and space, discretized energy stability, and efficiency of the proposed method.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2021)
Article
Mathematics, Applied
Dominik Schotzau, Carlo Marcati, Christoph Schwab
Summary: In this study, mixed hp-discontinuous Galerkin approximations of the stationary, incompressible Navier-Stokes equations on a polygonal subset Omega of R-2 are considered, with no-slip boundary conditions. By using corner-refined meshes and hp spaces with linearly increasing polynomial degrees, exponential rates of convergence of the method are proven for small data with piecewise analytic properties, based on recent results on analytic regularity of Leray solutions.
IMA JOURNAL OF NUMERICAL ANALYSIS
(2021)
Article
Computer Science, Interdisciplinary Applications
F. Massa, L. Ostrowski, F. Bassi, C. Rohde
Summary: This study introduces a novel exact Riemann solver based on an artificial Equation of State for the incompressible Euler equations, overcoming pressure-velocity coupling issues and fitting into the framework of hyperbolic conservation laws. Evaluation and analysis of the solver on 1D and 2D test cases demonstrate its effectiveness in high-order accurate discretization schemes.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Mustafa E. Danis, Jue Yan
Summary: This study proposes a new formula for the nonlinear viscous numerical flux and extends it to the compressible Navier-Stokes equations using the direct discontinuous Galerkin method with interface correction (DDGIC). The new method simplifies the implementation and enables accurate calculation of physical quantities.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Engineering, Multidisciplinary
Guanghui Hu, Ruo Li, Xiaohua Zhang
Summary: A novel stabilized meshless method is proposed for solving steady incompressible fluid flow problems, which simplifies the variational multiscale element free Galerkin method while retaining its advantages and avoiding the LBB condition. The method can automatically obtain the stabilization tensor and has been validated with various flow problems, showing numerical stability and accuracy while reducing computational cost compared to existing methods.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2021)
Article
Physics, Mathematical
S. Kelbij Star, Giovanni Stabile, Francesco Belloni, Gianluigi Rozza, Joris Degroote
Summary: A Finite-Volume based POD-Galerkin reduced order model is developed for fluid dynamics problems, with boundary conditions controlled using two different strategies: the lifting function method and penalty method. Comparison and testing show that both methods can effectively control the boundaries of the reduced order model, achieving the same level of accuracy in velocity and pressure fields.
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
(2021)
Article
Physics, Fluids & Plasmas
Y. Y. Liu, L. M. Yang, C. Shu, H. W. Zhang
Summary: This paper introduces an efficient high-order method based on radial basis functions and differential quadrature-finite volume for numerical simulation of incompressible flow on unstructured grids. The method approximates the solution within each control cell using a high-order polynomial and approximates derivatives using a mesh-free radial basis-function-based differential quadrature method. The lattice Boltzmann flux solver is applied to compute inviscid and viscous fluxes at cell interfaces simultaneously, contributing to improved computational efficiency.
Article
Mathematics, Applied
Aikaterini Aretaki, Efthymios N. Karatzas, Georgios Katsouleas
Summary: This work presents an analysis of an unfitted discontinuous Galerkin discretization method for solving the Stokes system. The method utilizes high-order discontinuous velocities and pressures and combines advantages of accurate approximation and flexibility in handling complex geometries. The approach includes a fictitious domain framework, pressure stabilization, and ghost penalty strategies to enhance stability and robustness. The study investigates inf-sup stability, convergence order, and sensitivity to cut configuration, and provides numerical examples to verify the theoretical results.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Chen Liu, Florian Frank, Beatrice M. Riviere
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2019)
Article
Computer Science, Interdisciplinary Applications
Chen Liu, Florian Frank, Christopher Thiele, Faruk O. Alpak, Steffen Berg, Walter Chapman, Beatrice Riviere
JOURNAL OF COMPUTATIONAL PHYSICS
(2020)
Article
Engineering, Multidisciplinary
Florian Frank, Andreas Rupp, Dmitri Kuzmin
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2020)
Article
Water Resources
Cristian D. Alecsa, Imre Boros, Florian Frank, Peter Knabner, Mihai Nechita, Alexander Prechtel, Andreas Rupp, Nicolae Suciu
ADVANCES IN WATER RESOURCES
(2020)
Article
Physics, Mathematical
Balthasar Reuter, Andreas Rupp, Vadym Aizinger, Florian Frank, Peter Knabner
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
(2020)
Article
Mathematics, Applied
Balthasar Reuter, Hennes Hajduk, Andreas Rupp, Florian Frank, Vadym Aizinger, Peter Knabner
Summary: This paper documents the current state of development and applications of the open-source toolbox FESTUNG for solving partial differential equations using MATLAB/GNU Octave. The goal is to provide a user-friendly and computationally efficient software tool for research and teaching purposes.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Computer Science, Interdisciplinary Applications
Deep Ray, Chen Liu, Beatrice Riviere
Summary: A numerical method using discontinuous polynomial approximations is formulated to solve a phase-field model of two immiscible fluids with a soluble surfactant. The proposed scheme is shown to decay the total free Helmholtz energy at the discrete level, consistent with the continuous model dynamics, and recovers the Langmuir adsorption isotherms at equilibrium. Simulations of various flow scenarios demonstrate the dynamics of flow with and without surfactant, and the method is successfully applied to simulate fluid flows in the pore space of Berea sandstone obtained by micro-CT imaging.
COMPUTATIONAL GEOSCIENCES
(2021)
Article
Mathematics, Applied
Philipp Werner, Martin Burger, Florian Frank, Harald Garcke
Summary: The aim of this paper is to develop suitable models for cell blebbing phenomenon and predict the mechanical effects, including the interaction between cell membrane and actin cortex. A two-phase field model is employed, which uses diffuse descriptions of both membrane and cortex and allows for a proper description of interaction via linker protein densities. In addition to the detailed modeling, some energetic aspects of the models are discussed, and a numerical scheme is presented for computational studies. The results demonstrate that several effects found in experiments, particularly bleb formation by cortex rupture, can be reproduced, which was not possible with previous models lacking linker dynamics.
SIAM JOURNAL ON APPLIED MATHEMATICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Stephan Gaerttner, Faruk O. Alpak, Andreas Meier, Nadja Ray, Florian Frank
Summary: This paper proposes a novel methodology for permeability prediction from micro-CT scans of geological rock samples. By using direct numerical simulation (DNS) to solve the stationary Stokes equation, the convergence issues of lattice Boltzmann methods (LBM) on complex pore geometries are circumvented, resulting in improved generality and accuracy of the training data set. The physics-informed CNN (PhyCNN) is trained using DNS-computed permeabilities and additional information about confined structures, achieving high prediction accuracy.
COMPUTATIONAL GEOSCIENCES
(2023)
Correction
Computer Science, Interdisciplinary Applications
Stephan Gaerttner, Faruk O. Alpak, Andreas Meier, Nadja Ray, Florian Frank
COMPUTATIONAL GEOSCIENCES
(2023)
Article
Mathematics, Interdisciplinary Applications
Moritz Hauck, Vadym Aizinger, Florian Frank, Hennes Hajduk, Andreas Rupp
GEM-INTERNATIONAL JOURNAL ON GEOMATHEMATICS
(2020)
Article
Computer Science, Interdisciplinary Applications
Tian Liang, Lin Fu
Summary: In this work, a new shock-capturing framework is proposed based on a new candidate stencil arrangement and the combination of infinitely differentiable non-polynomial RBF-based reconstruction in smooth regions with jump-like non-polynomial interpolation for genuine discontinuities. The resulting scheme achieves high order accuracy and resolves genuine discontinuities with sub-cell resolution.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Lukas Lundgren, Murtazo Nazarov
Summary: In this paper, a high-order accurate finite element method for incompressible variable density flow is introduced. The method addresses the issues of saddle point system and stability problem through Schur complement preconditioning and artificial compressibility approaches, and it is validated to have high-order accuracy for smooth problems and accurately resolve discontinuities.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Gabriele Ciaramella, Laurence Halpern, Luca Mechelli
Summary: This paper presents a novel convergence analysis of the optimized Schwarz waveform relaxation method for solving optimal control problems governed by periodic parabolic PDEs. The analysis is based on a Fourier-type technique applied to a semidiscrete-in-time form of the optimality condition, which enables a precise characterization of the convergence factor at the semidiscrete level. The behavior of the optimal transmission condition parameter is also analyzed in detail as the time discretization approaches zero.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jonas A. Actor, Xiaozhe Hu, Andy Huang, Scott A. Roberts, Nathaniel Trask
Summary: This article introduces a scientific machine learning framework that uses a partition of unity architecture to model physics through control volume analysis. The framework can extract reduced models from full field data while preserving the physics. It is applicable to manifolds in arbitrary dimension and has been demonstrated effective in specific problems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Nozomi Magome, Naoki Morita, Shigeki Kaneko, Naoto Mitsume
Summary: This paper proposes a novel strategy called B-spline based SFEM to fundamentally solve the problems of the conventional SFEM. It uses different basis functions and cubic B-spline basis functions with C-2-continuity to improve the accuracy of numerical integration and avoid matrix singularity. Numerical results show that the proposed method is superior to conventional methods in terms of accuracy and convergence.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Timothy R. Law, Philip T. Barton
Summary: This paper presents a practical cell-centred volume-of-fluid method for simulating compressible solid-fluid problems within a pure Eulerian setting. The method incorporates a mixed-cell update to maintain sharp interfaces, and can be easily extended to include other coupled physics. Various challenging test problems are used to validate the method, and its robustness and application in a multi-physics context are demonstrated.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Xing Ji, Fengxiang Zhao, Wei Shyy, Kun Xu
Summary: This paper presents the development of a third-order compact gas-kinetic scheme for compressible Euler and Navier-Stokes solutions, constructed particularly for an unstructured tetrahedral mesh. The scheme demonstrates robustness in high-speed flow computation and exhibits excellent adaptability to meshes with complex geometrical configurations.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Alsadig Ali, Abdullah Al-Mamun, Felipe Pereira, Arunasalam Rahunanthan
Summary: This paper presents a novel Bayesian statistical framework for the characterization of natural subsurface formations, and introduces the concept of multiscale sampling to localize the search in the stochastic space. The results show that the proposed framework performs well in solving inverse problems related to porous media flows.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jacob Rains, Yi Wang, Alec House, Andrew L. Kaminsky, Nathan A. Tison, Vamshi M. Korivi
Summary: This paper presents a novel method called constrained optimized DMD with Control (cOptDMDc), which extends the optimized DMD method to systems with exogenous inputs and can enforce the stability of the resulting reduced order model (ROM). The proposed method optimally places eigenvalues within the stable region, thus mitigating spurious eigenvalue issues. Comparative studies show that cOptDMDc achieves high accuracy and robustness.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Andrea La Spina, Jacob Fish
Summary: This work introduces a hybridizable discontinuous Galerkin formulation for simulating ideal plasmas. The proposed method couples the fluid and electromagnetic subproblems monolithically based on source and employs a fully implicit time integration scheme. The approach also utilizes a projection-based divergence correction method to enforce the Gauss laws in challenging scenarios. Numerical examples demonstrate the high-order accuracy, efficiency, and robustness of the proposed formulation.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Junhong Yue, Peijun Li
Summary: This paper proposes two numerical methods (IP-FEM and BP-FEM) to study the flexural wave scattering problem of an arbitrary-shaped cavity on an infinite thin plate. These methods successfully decompose the fourth-order plate wave equation into the Helmholtz and modified Helmholtz equations with coupled conditions on the cavity boundary, providing an effective solution to this challenging problem.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
William Anderson, Mohammad Farazmand
Summary: We develop fast and scalable methods, called RONS, for computing reduced-order nonlinear solutions. These methods have been proven to be highly effective in tackling challenging problems, but become computationally prohibitive as the number of parameters grows. To address this issue, three separate methods are proposed and their efficacy is demonstrated through examples. The application of RONS to neural networks is also discussed.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Marco Caliari, Fabio Cassini
Summary: In this paper, a second order exponential scheme for stiff evolutionary advection-diffusion-reaction equations is proposed. The scheme is based on a directional splitting approach and uses computation of small sized exponential-like functions and tensor-matrix products for efficient implementation. Numerical examples demonstrate the advantage of the proposed approach over state-of-the-art techniques.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Sebastiano Boscarino, Seung Yeon Cho, Giovanni Russo
Summary: This work proposes a high order conservative semi-Lagrangian method for the inhomogeneous Boltzmann equation of rarefied gas dynamics. The method combines a semi-Lagrangian scheme for the convection term, a fast spectral method for computation of the collision operator, and a high order conservative reconstruction and a weighted optimization technique to preserve conservative quantities. Numerical tests demonstrate the accuracy and efficiency of the proposed method.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jialei Li, Xiaodong Liu, Qingxiang Shi
Summary: This study shows that the number, centers, scattering strengths, inner and outer diameters of spherical shell-structured sources can be uniquely determined from the far field patterns. A numerical scheme is proposed for reconstructing the spherical shell-structured sources, which includes a migration series method for locating the centers and an iterative method for computing the inner and outer diameters without computing derivatives.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)