Related papers: A New Mode Reduction Strategy for the Generalized …
It is essential to efficiently solve multiscale flows covering the continuum regime to the rarefied regime. The explicit form of Grad's 13 moments distribution function-based moment gas kinetic solver (G13-MGKS) has been proposed in our…
Within the Functional Renormalisation Group (FRG) approach, we present a fluid-dynamical approach to solving flow equations for models living in a multi-dimensional field space. To this end, the underlying exact flow equation of the…
In this paper, to solve a broad class of complex symmetric linear systems, we recast the complex system in a real formulation and apply the generalized successive overrelaxation (GSOR) iterative method to the equivalent real system. We then…
A new slender-body theory for viscous flow, based on the concepts of dimensional reduction and hyperviscous regularization, is presented. The geometry of flat, elongated, or point-like rigid bodies immersed in a viscous fluid is…
In this article, we consider a novel version of three-dimensional (3D) globally modified Navier-Stokes (GMNS) system introduced by [Caraballo et. al., Adv. Nonlinear Stud. (2006), 6:411-436], which is very significant from the perspective…
3D Gaussian Splatting (3DGS) has emerged as a promising approach for 3D scene representation, offering a reduction in computational overhead compared to Neural Radiance Fields (NeRF). However, 3DGS is susceptible to high-frequency artifacts…
The paper proposes a new, conservative fully-discrete scheme for the numerical solution of the regularised shallow water Boussinesq system of equations in the cases of periodic and reflective boundary conditions. The particular system is…
Generalized Hydrodynamics (GHD) has recently been devised as a method to solve the dynamics of integrable quantum many-body systems beyond the mean-field approximation. In its original form, a major limitation is the inability to predict…
We extend previous work [Y. E. Litvinenko, Phys. Plasmas 17, 074502 (2010)] on a direct method for finding similarity reductions of partial differential equations such as the Grad-Shafranov equation, to the case of the generalized…
Simulations of chaotic systems can only produce high-fidelity trajectories if the initial and boundary conditions are well specified. When these conditions are unknown but measurements are available, variational state estimation can…
Explicit time integration for immersed finite element discretizations severely suffers from the influence of poorly cut elements. In this contribution, we propose a generalized eigenvalue stabilization (GEVS) strategy for the element mass…
In this paper, we propose a new hybridized discontinuous Galerkin (DG) method for the convection-diffusion problems with mixed boundary conditions. A feature of the proposed method, is that it can greatly reduce the number of…
The notion of signal sparsity has been gaining increasing interest in information theory and signal processing communities. As a consequence, a plethora of sparsity metrics has been presented in the literature. The appropriateness of these…
Renormalization-group (RG) flow equations have been derived for the generalized sine-Gordon model (GSGM) and the Coulomb gas (CG) in d >= 3 of dimensions by means of Wegner's and Houghton's, and by way of the real-space RG approaches. The…
For increasingly rarefied flowfields, the Navier-Stokes (NS) equations lose accuracy partially due to the single temperature approximation. To overcome this barrier, a continuum multi-temperature model based on the Bhatnagar-Gross-Krook…
We introduce a modified Consensus-Based Optimization model that admits a fully unified and rigorous analysis of its finite-particle dynamics, the associated McKean--Vlasov equation, and their optimization behavior under a single set of…
Inference and simulation in the context of high-dimensional dynamical systems remain computationally challenging problems. Some form of dimensionality reduction is required to make the problem tractable in general. In this paper, we propose…
Region-of-Interest (ROI)-based image compression allocates bits unevenly according to the semantic importance of different regions. Such differentiated coding typically induces a sharp-peaked and heavy-tailed distribution. This distribution…
Most high order computational fluid dynamics (CFD) methods for compressible flows are based on Riemann solver for the flux evaluation and Runge-Kutta (RK) time stepping technique for temporal accuracy. The main advantage of this kind of…
We present a theoretical model that fully supports the recently disclosed generalized droop formula (GDF) for calculating the signal-to-noise ratio (SNR) of constant-output power (COP) amplified dispersion-uncompensated coherent links…