Related papers: A space-time smooth artificial viscosity method wi…
We propose a new kind of localized shock capturing for continuous (CG) and discontinuous Galerkin (DG) discretizations of hyperbolic conservation laws. The underlying framework of dissipation-based weighted essentially nonoscillatory (WENO)…
A numerical analysis of the effect of artificial viscosity is undertaken in order to understand the effect of numerical diffusion on numerical boundary feedback control. The analysis is undertaken on the linear hyperbolic systems…
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…
In this work, we derive particle schemes, based on micro-macro decomposition, for linear kinetic equations in the diffusion limit. Due to the particle approximation of the micro part, a splitting between the transport and the collision part…
The artificial viscosity is reconsidered in smoothed particle hydrodynamics to prevent inter-particle penetration, unwanted heating, and unphysical solutions. The coefficients in the Monaghan's standard artificial viscosity are considered…
We introduce a novel artificial compressibility technique to approximate the incompressible Navier-Stokes equations with variable fluid properties such as density and dynamical viscosity. The proposed scheme used the couple pressure and…
We analyse and improve the volume-penalty method, a simple and versatile way to model objects in fluid flows. The volume-penalty method is a kind of fictitious-domain method that approximates no-slip boundary conditions with rapid linear…
Using the Stochastic Adhesion Model (SAM) as a simple toy model for cosmic structure formation, we study renormalization and the removal of the cutoff dependence from loop integrals in perturbative calculations. SAM shares the same symmetry…
This work describes three diffuse-interface methods for the simulation of immiscible, compressible multiphase fluid flows and elastic-plastic deformation in solids. The first method is the localized-artificial-diffusivity approach of Cook…
The noise generated by the friction of two rough surfaces under weak contact pressure is usually called roughness noise. The underlying vibration which produces the noise stems from numerous instantaneous shocks (in the microsecond range)…
Accurate modeling of sea ice dynamics is critical for predicting environmental variables and is important in applications such as navigating ice breaker ships. Research for both modeling and simulating sea ice dynamics is ongoing, with the…
The shock instability problem commonly arises in flow simulations involving strong shocks, particularly when employing high-order schemes, limiting their applications in hypersonic flow simulations. This study focuses on exploring the…
The proposed method aims to approximate a solution of a fluid-fluid interaction problem in case of low viscosities. The nonlinear interface condition on the joint boundary allows for this problem to be viewed as a simplified version of the…
We present a novel mapping approach for WENO schemes through the use of an approximate constant mapping function which is constructed by employing an approximation of the classic signum function. The new approximate constant mapping…
The vaporization of a freely moving drop in a uniform, high-temperature gas stream is investigated through direct numerical simulation. The incompressible Navier-Stokes equations with surface tension and phase change are solved in…
In the present work, we propose two new variants of fifth order finite difference WENO schemes of adaptive order. We compare our proposed schemes with other variants of WENO schemes with special emphasize on WENO-AO(5,3) scheme [Balsara,…
Time discretization along with space discretization is important in the numerical simulation of subsurface flow applications for long run. In this paper, we derive theoretical convergence error estimates in discrete-time setting for…
The effects induced by numerical schemes and mesh geometry on the solution of two-dimensional supersonic inviscid flows are investigated in the context of the compressible Euler equations. Five different finite-difference schemes are…
We present a new perspective on the use of weighted essentially nonoscillatory (WENO) reconstructions in high-order methods for scalar hyperbolic conservation laws. The main focus of this work is on nonlinear stabilization of continuous…
The lack of smoothness is a common feature of weak solutions of nonlinear hyperbolic equations and is a crucial issue in their approximation. This has motivated several efforts to define appropriate indicators, based on the values of the…