Related papers: Spectral Difference method with a posteriori limit…
A highly efficient three-dimensional (3D) Lattice Boltzmann (LB) model for high speed compressible flows is proposed. This model is developed from the original one by Kataoka and Tsutahara[Phys. Rev. E 69, 056702 (2004)]. The convection…
Least squares deconvolution (LSD) is a powerful method of extracting high-precision average line profiles from the stellar intensity and polarization spectra. Despite its common usage, the LSD method is poorly documented and has never been…
We present a scalable Bayesian framework for the analysis of confocal fluorescence spectroscopy data, addressing key limitations in traditional fluorescence correlation spectroscopy methods. Our framework captures molecular motion,…
High-order finite volume and finite element methods offer impressive accuracy and cost efficiency when solving hyperbolic conservation laws with smooth solutions. However, if the solution contains discontinuities, these high-order methods…
Spectral deferred corrections (SDC) is an iterative approach for constructing higher- order accurate numerical approximations of ordinary differential equations. SDC starts with an initial approximation of the solution defined at a set of…
We propose a direct numerical method for the solution of an optimal control problem governed by a two-side space-fractional diffusion equation. The presented method contains two main steps. In the first step, the space variable is…
For the past 20 years, our approach to shock capturing in smoothed particle hydrodynamics (SPH) has been to use artificial viscosity and conductivity terms supplemented by switches to control excess dissipation away from shocks (Monaghan…
Splitting methods are a widely used numerical scheme for solving convection-diffusion problems. However, they may lose stability in some situations, particularly when applied to convection-diffusion problems in the presence of an unbounded…
High order discretization schemes play more important role in fractional operators than classical ones. This is because usually for classical derivatives the stencil for high order discretization schemes is wider than low order ones; but…
We present the Method Of Lines (MOL), which is based on the spectral collocation method, to solve space-fractional advection-diffusion equations (SFADEs) on a finite domain with variable coefficients. We focus on the cases in which the…
Context. The anelastic approximation is often adopted in numerical calculation with low Mach number, such as stellar internal convection. This approximation requires frequent global communication, because of an elliptic partial differential…
We build a multi-element variant of the smoothness increasing accuracy conserving (SIAC) shock capturing technique proposed for single element spectral methods by Wissink et al. (B.W. Wissink, G.B. Jacobs, J.K. Ryan, W.S. Don, and E.T.A.…
In this paper, we consider the initial boundary value problem of the two dimensional multi-term time fractional mixed diffusion and diffusion-wave equations. An alternating direction implicit (ADI) spectral method is developed based on…
A general procedure to construct a class of simple and efficient high resolution Total Variation Diminishing (TVD) schemes for non-linear hyperbolic conservation laws by introducing anti-diffusive terms with the flux limiters is presented.…
Spectral imaging is a fundamental diagnostic technique with widespread application. Conventional spectral imaging approaches have intrinsic limitations on spatial and spectral resolutions due to the physical components they rely on. To…
We introduce a novel positivity-preserving, parameter-free numerical stabilisation approach for high-order discontinuous spectral element approximations of compressible multi-species flows. The underlying stabilisation method is the…
In this paper, we have solved 1D special relativistic hydrodynamical equations using different numerical method in computational gas dynamics. The numerical solutions of these equations for smooth wave cases give better solution when we use…
We are interested in the numerical solution of large systems of hyperbolic conservation laws or systems in which the characteristic decomposition is expensive to compute. Solving such equations using finite volumes or Discontinuous Galerkin…
This paper proposes a novel numerical method based on Godunov Smoothed Particle Hydrodynamics for special relativistic fluid dynamics. Our method utilizes a Riemann solver to describe shock, enhancing accuracy in strong shock waves. The…
We develop well-balanced central schemes on overlapping cells for the Saint-Venant shallow water system and its variants. The main challenge in deriving the schemes is related to the fact that the Saint-Venant system contains a geometric…