Related papers: A space-time smooth artificial viscosity method wi…
In this first part of two papers, we extend the C-method developed in [40] for adding localized, space-time smooth artificial viscosity to nonlinear systems of conservation laws that propagate shock waves, rarefaction waves, and contact…
We introduce a new methodology for adding localized, space-time smooth, artificial viscosity to nonlinear systems of conservation laws which propagate shock waves, rarefactions, and contact discontinuities, which we call the $C$-method. We…
This contribution Part II of a two-part series, extends the general-domain FC-SDNN (Fourier Continuation Shock-Detecting Neural Network) introduces in Part I to enable treatment of non-smooth domains, it introduces a parallel implementation…
In physically inviscid fluid dynamics, "shock capturing" methods adopt either an artificial viscosity contribution or an appropriate Riemann solver algorithm. These techniques are necessary to solve the strictly hyperbolic Euler equations…
In the physically non viscous fluid dynamics, "shock capturing" methods adopt either an artificial viscosity contribution or an appropriate Riemann solver algorithm. These techniques are necessary to solve the strictly hyperbolic Euler…
In this work, a localized artificial-viscosity/diffusivity method is proposed for accurately capturing discontinuities in compressible flows. There have been numerous efforts to improve the artificial diffusivity formulation in the last two…
In this work, a one-dimensional simulation code was developed for both single-phase and two-phase systems, focusing on time-dependent Euler equations for gas and particles. These equations, non-linear hyperbolic conservation laws, describe…
We investigate the large-scale influence of numerical noises as tiny artificial stochastic disturbances on a sustained turbulence. Using the two-dimensional (2D) turbulent Rayleigh-B\'enard (RB) convection as an example, we numerically…
We introduce an adaptive viscosity regularization approach for the numerical solution of systems of nonlinear conservation laws with shock waves. The approach seeks to solve a sequence of regularized problems consisting of the system of…
In smooth-particle hydrodynamics (SPH), artificial viscosity is necessary for the correct treatment of shocks, but often generates unwanted dissipation away from shocks. We present a novel method of controlling the amount of artificial…
In this paper, we study the dynamics of a two-dimensional viscous fluid evolving through a porous medium or a Hele-Shaw cell, driven by gravity and surface tension. A key feature of this study is that the fluid is confined within a vessel…
In the recent paper, the global-in-time inviscid limit of the three-dimensional (3D) isentropic compressible Navier-Stokes equations is considered. First, when viscosity coefficients are given as a constant multiple of density's power…
This paper presents a spectral scheme for the numerical solution of nonlinear conservation laws in non-periodic domains under arbitrary boundary conditions. The approach relies on the use of the Fourier Continuation (FC) method for spectral…
In 2001, Bertalmio et. al. drew an analogy between the image intensity function for the image inpainting problem and the stream function in a two-dimensional (2D) incompressible fluid. An approximate solution to the inpainting problem is…
We analyze the shock formation process for the 3d non-isentropic Euler equations with the ideal gas law, in which sounds waves interact with entropy waves to produce vorticity. Building on our theory for isentropic flows in [3,4], we give a…
In the non viscous fluid dynamics, Smooth Particle Hydrodynamics (SPH), as a free Lagrangian "shock capturing" method adopts either an artificial viscosity contribution or an appropriate Riemann solver technique. An explicit or an implicit…
We propose a high-order spacetime wavelet method for the solution of nonlinear partial differential equations with a user-prescribed accuracy. The technique utilizes wavelet theory with a priori error estimates to discretize the problem in…
Numerical simulation of viscoelastic flows is challenging because of the hyperbolic nature of viscoelastic constitutive equations. Despite their superior accuracy and efficiency, pseudo-spectral methods require the introduction of…
The artificial viscosity approach for curing the carbuncle phenomenon (a numerical problem, also known as the shock instability) in shock-capturing methods has been recently presented and successfully tested on the first-order schemes in…
This paper presents an alternative formulation of the ASPH algorithm for evolving anisotropic smoothing kernels, in which the geometric approach of Shapiro et al. (1996; Paper I) is replaced by an approach involving a local transformation…