A two-dimensional mountainous mass flow dynamic procedure solver (Massflow-2D) using the MacCormack-TVD finite difference scheme is proposed. The solver is implemented in Matlab on structured meshes with variable computational domain. To verify the model, a variety of numerical test scenarios, namely, the classical one-dimensional and two-dimensional dam break, the landslide in Hong Kong in 199...

It was recently shown that for reasonable notions of approximation of states and functions by quantum circuits, almost all states and functions are exponentially hard to approximate 5]. The bounds obtained are asymptotically tight except for the one based on total variation distance (TVD). TVD is the most relevant metric for the performance of a quantum circuit. In this paper we obtain asymptot...

 Abstract—The cylindrically converging shock wave was numerically simulated by solving the Euler equations in cylindrical coordinates with TVD scheme and MUSCL [1] approach, using Roe's approximate Riemann solver [2] and super-bee nonlinear limiter [3]. The present study used the in house code developed for this purpose. The behavior of the solution in the vicinity of axis is investigated and ...

A mathematical model for turbulent gas-liquid flows with mass transfer and chemical reactions is presented and a robust solution strategy based on nested iterations is proposed for the numerical treatment of the intricately coupled PDEs. In particular, the incompressible Navier-Stokes equations are solved by a discrete projection scheme from the family of Pressure Schur Complement methods. Nove...

This article deals with a method, based on total variation diminishing (TVD) scheme, for solving three-dimensional equations of gravitational gas dynamics. For this method a parallel algorithm of the decision is offered. Equations of this kind are a powerful approach to simulating astrophysical problems. Numerical schemes applied for their solving must provide high-resolution capturing of shock...

The algebraic flux correction (AFC) paradigm is extended to finite element discretizations with a consistent mass matrix. A nonoscillatory low-order scheme is constructed by resorting to mass lumping and conservative elimination of negative off-diagonal coefficients from the discrete transport operator. In order to recover the high accuracy of the original Galerkin scheme, a limited amount of c...

The discrete ordinates method (DOM) and finitevolume method (FVM) are used extensively to solve the radiative transfer equation (RTE) in furnaces and combusting mixtures due to their balance between numerical efficiency and accuracy. These methods are typically solved using space-marching techniques since they converge rapidly for constant coefficient spatial discretization schemes and non-scat...

We describe a newly developed cosmological hydrodynamics code based on the weighted essentially non-oscillatory (WENO) schemes for hyperbolic conservation laws. High order finite difference WENO schemes are designed for problems with piecewise smooth solutions containing discontinuities, and have been successful in applications for problems involving both shocks and complicated smooth solution ...