Related papers: New Adaptive Low-Dissipation Central-Upwind Scheme…
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…
Numerical simulation of multi-component flow systems characterized by the simultaneous presence of pressure-velocity coupling and pressure-density coupling dominated regions remains a significant challenge in computational fluid dynamics.…
In this article we consider one-dimensional random systems of hyperbolic conservation laws. We first establish existence and uniqueness of random entropy admissible solutions for initial value problems of conservation laws which involve…
When extended to two-phase flows, weakly compressible models lead to a non-conservative system, which precludes its treatment using standard finite volume techniques. In this paper, a novel HLLC-type path-conservative scheme is formulated…
An explicit moving boundary method for the numerical solution of time-dependent hyperbolic conservation laws on grids produced by the intersection of complex geometries with a regular Cartesian grid is presented. As it employs directional…
We present a new family of high-order shock-capturing finite difference numerical methods for systems of conservation laws. These methods, called Adaptive Compact Approximation Taylor (ACAT) schemes, use centered $(2p + 1)$-point stencils,…
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…
This paper contributes to the exploration of a recently introduced computational paradigm known as second-order flows, which are characterized by novel dissipative hyperbolic partial differential equations extending accelerated gradient…
High-order Godunov methods for gas dynamics have become a standard tool for simulating different classes of astrophysical flows. Their accuracy is mostly determined by the spatial interpolant used to reconstruct the pair of Riemann states…
Numerical simulation of compressible fluid flows is performed using the Euler equations. They include the scalar advection equation for the density, the vector advection equation for the velocity and a given pressure dependence on the…
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…
We assess the suitability of a recent high-resolution central scheme developed by Kurganov & Tadmor (2000) for the solution of the relativistic hydrodynamics equations. The novelty of this approach relies on the absence of Riemann solvers…
In this paper, we investigate adaptive streamline upwind/Petrov Galerkin (SUPG) methods for singularly perturbed convection-diffusion-reaction equations in a new dual norm presented in [Du and Zhang, J. Sci. Comput. (2015)]. The flux is…
In this work, we introduce two novel reformulations of a recent weakly hyperbolic model for two-phase flow with surface tension. In the model, the tracking of phase boundaries is achieved by using a vector interface field, rather than a…
This article presents two novel adaptive-sparse polynomial dimensional decomposition (PDD) methods for solving high-dimensional uncertainty quantification problems in computational science and engineering. The methods entail global…
We introduced the least-squares ReLU neural network (LSNN) method for solving the linear advection-reaction problem with discontinuous solution and showed that the method outperforms mesh-based numerical methods in terms of the number of…
A quasi-second order scheme is developed to obtain approximate solutions of the shallow water equationswith bathymetry. The scheme is based on a staggered finite volume scheme for the space discretization:the scalar unknowns are located in…
This paper presents an arbitrary h.o. accurate ADER DG method on space-time adaptive meshes (AMR) for the solution of two important families of non-linear time dependent PDE for compr. dissipative flows: the compr. Navier-Stokes equations…
In this thesis we propose a novel method to compute higher-order corrections to physical cross sections, bypassing more traditional approaches. This technique, the Four-Dimensional Unsubtraction (FDU), is based on the Loop-Tree Duality…
We introduce a second-order numerical scheme for compressible atmospheric motions at small to planetary scales. The collocated finite volume method treats the advection of mass, momentum, and mass-weighted potential temperature in…