Article
Computer Science, Interdisciplinary Applications
Gabor Toth
Summary: We propose a new principle for numerical schemes of conservation laws in one and multiple dimensions. The new formulation is based on the concept of Total of Time Variation (TOTV), which is defined as the volume integral of the magnitude of the time derivative. We show that TOTV is a conserved quantity for both one-dimensional and multi-dimensional scalar conservation laws. We introduce the Total of Time Variation Diminishing (TOTVD) method, which ensures that the discrete form of TOTV does not increase with time, making the scheme stable against catastrophic instabilities.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Yusuke Majima, Hiro Wakimura, Takayuki Aoki, Feng Xiao
Summary: This paper proposes an adaptive model for determining the suitable limiter function in compressible flow simulations to ensure numerical accuracy and stability.
COMPUTERS & FLUIDS
(2023)
Article
Computer Science, Interdisciplinary Applications
Yoshiaki Abe, Ziyao Sun, Feng Xiao
Summary: A novel approach for selecting appropriate reconstructions is implemented to address the failure of high-order polynomial approximation in capturing strong discontinuities. The boundary variation diminishing reconstruction algorithm can achieve oscillation suppression and numerical dissipation in one-dimensional linear advection and nonlinear system equations.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2021)
Article
Automation & Control Systems
Christian Grussler, Rodolphe Sepulchre
Summary: This paper examines the variation diminishing property of k-positive linear time-invariant (LTI) systems, focusing on the discrete-time Toeplitz and Hankel operators of finite dimensional causal systems. The main finding is that these operators can be approximated dominantly by a series or parallel interconnections of k first order positive systems. Additionally, the k-positivity of an LTI system can be expressed as the external positivity of k compound LTI systems, which extends the well-known properties of externally positive systems and totally positive systems. These results also apply to continuous-time systems.
Article
Computer Science, Interdisciplinary Applications
Amareshwara Sainadh Chamarthi, Steven H. Frankel
Summary: In this paper, a novel hybrid nonlinear explicit-compact scheme for shock capturing based on a boundary variation diminishing (BVD) reconstruction is presented. The method combines a non-dissipative sixth-order central compact interpolation and a fifth-order monotonicity preserving scheme through the BVD algorithm. Numerical examples suggest that the method is capable of resolving small scale flow features and capturing sharp discontinuities as the MP5 scheme.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Computer Science, Artificial Intelligence
Antonin Chambolle, Thomas Pock
Summary: This work introduces a general framework for discrete approximations of total variation in image reconstruction, showing consistency in the sense of Gamma-convergence. Algorithms for learning discrete total variation are proposed to achieve optimal reconstruction quality for specific image reconstruction tasks. The study reveals significant differences in learned discretizations for different tasks, indicating that there is no universal best discretization method for total variation.
SIAM JOURNAL ON IMAGING SCIENCES
(2021)
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
Geosciences, Multidisciplinary
Young-Kwang Choi, Fengyan Shi, Matt Malej, Jane M. Smith, James T. Kirby, Stephan T. Grilli
Summary: This study develops a multigrid-nesting interface for the Boussinesq wave model FUNWAVE-TVD. The interface manages the time sequencing and two-way nesting processes between the parent and child grids, ensuring workload balance and efficient data management.
GEOSCIENTIFIC MODEL DEVELOPMENT
(2022)
Article
Mathematics, Applied
Corentin Caillaud, Antonin Chambolle
Summary: In this paper, we analyze the convergence rate of two different discretizations of the Rudin-Osher-Fatemi (ROF) denoising problem. The first discretization induces blurring in certain diagonal directions, while the second discretization based on dual Raviart-Thomas fields achieves an optimal convergence rate.
IMA JOURNAL OF NUMERICAL ANALYSIS
(2023)
Article
Mathematics, Applied
L'Ubomir Banas, Andre Wilke
Summary: This paper presents a posteriori error estimates for a fully discrete time-implicit finite element approximation of the stochastic total variation flow (STVF) with additive space time noise. The estimates are derived first for an implementable fully discrete approximation of a regularized STVF. It is then shown that the derived a posteriori estimates remain valid for the unregularized flow with a perturbation term controlled by the regularization parameter. Based on these estimates, a pathwise algorithm for adaptive space-time refinement is proposed and numerical simulations for the regularized STVF are performed to demonstrate the behavior of the proposed algorithm.
SIAM JOURNAL ON NUMERICAL ANALYSIS
(2022)
Article
Computer Science, Artificial Intelligence
Lukas Baumgaertner, Ronny Bergmann, Roland Herzog, Stephan Schmidt, Jose Vidal-Nunez
Summary: This paper proposes a novel discrete concept for TGV in image denoising, aiming to reduce the staircasing effect in classical total variation regularization. It describes a discrete, second-order TGV for piecewise constant functions on triangular meshes, allowing it to be used on more general data structures. Attention is given to the kernel of the TGV functional, which consists of linear polynomials. Numerical experiments demonstrate the effectiveness of this approach on images defined on nonstandard grids, including data from a three-dimensional scanner.
SIAM JOURNAL ON IMAGING SCIENCES
(2023)
Editorial Material
Environmental Sciences
Rebecca Finger-Higgens
Summary: Due to rising air temperatures and autumn rains, some Arctic lakes are drying, leading to permafrost thawing and water drainage.
NATURE CLIMATE CHANGE
(2022)
Article
Environmental Sciences
Steven Dewitte, Jan Cornelis, Mustapha Meftah
Summary: This study analyzed the space measurements of Total Solar Irradiance (TSI) and derived a regression model to reproduce the daily variations of TSI. The reconstruction of TSI based on the Sunspot Number confirmed the existence of a 105-year Gleissberg cycle, with the TSI level of the current grand minimum only slightly higher than that of the 18th century.
Article
Mathematics, Applied
A. J. Kriel
Summary: This study introduces a general condition for numerical schemes to mimic the properties of exact solutions of scalar conservation laws. By applying this condition to various schemes, different CFL-like conditions are derived to ensure the accuracy and reliability of the numerical simulations.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Thermodynamics
Jianhua Wu, Jiachen Li, Shuai Zhang
Summary: This paper focuses on the suction pressure pulsation in rotary compressor performance and emphasizes the importance of employing gas dynamic model for simulation to predict compressor performance and design structure. The study adopts the total variation diminishing scheme, which provides faster convergence speed and less dispersion compared to the conventional Lax-wendroff two-step (LW2) scheme. Additionally, the one-dimensional model is used to update the traditional zero-dimensional model for the accumulator, resulting in more accurate pressure results at the suction pipe inlet. The simulation results are compared with experimental data, showing high Pearson Correlation Coefficients and low relative errors, indicating better agreement on pressure pulsation simulation and performance prediction.
PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART A-JOURNAL OF POWER AND ENERGY
(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)
