Related papers: Validation of a high-order finite difference compr…
We discuss the solution of regular and singular Sturm-Liouville problems by means of High Order Finite Difference Schemes. We describe a code to define a discrete problem and its numerical solution by means of linear algebra techniques.…
The satisfiability and optimization of finite-dimensional Boolean formulas are studied using percolation theory, rare region arguments, and boundary effects. In contrast with mean-field results, there is no satisfiability transition, though…
A computationally efficient high-order solver is developed to compute the wall distances by solving the relevant partial differential equations, namely: Eikonal, Hamilton-Jacobi (HJ) and Poisson equations. In contrast to the upwind schemes…
We compare some first order well-balanced numerical schemes for shallow water system with special interest in applications where there are abrupt variations of the topography. We show that the space step required to obtain a prescribed…
We derive and analyse well-posed boundary conditions for the linear shallow water wave equation. The analysis is based on the energy method and it identifies the number, location and form of the boundary conditions so that the initial…
We discuss in detail a recently proposed hybrid particle-continuum scheme for complex fluids and evaluate it at the example of a confined homopolymer solution in slit geometry. The hybrid scheme treats polymer chains near the impenetrable…
To simulate the expansion of the matter created in relativistic nuclear collisions, codes in 3+1 dimensions are used and we are developing a new one. To benchmark such codes, the Sod's shock tube is often used. A closely related problem is…
Passive scalar dynamics in wall-bounded turbulence is studied via Direct Numerical Simulations of plane channel flow, for a friction Reynolds number $Re_* = 160$ and a Schmidt number $Sc=1$. Peculiar to the present research is that the…
The unavailability of accurate boundary treatment methods for compressible Smoothed Particle Hydrodynamics (SPH) severely limits its ability to simulate flows in and around bodies. To this end, challenges specific to compressible flows with…
This paper is concerned with the inflow problem for the one-dimensional compressible Navier-Stokes equations. For such a problem, F. M. Huang, A. Matsumura and X. D. Shi showed that there exists viscous shock wave solution to the inflow…
Polymer chains undergoing a continuous adsorption-desorption transition are studied through extensive computer simulations. A three-dimensional self-avoiding walk lattice model of a polymer chain grafted onto a surface has been treated for…
We construct a new compact semi-explicit three-level in time fourth-order finite-difference scheme for numerical solving the general multidimensional acoustic wave equation, where both the speed of sound and density of a medium are…
We present the existence/non-existence criteria for large-amplitude boundary layer solutions to the inflow problem of the one-dimensional (1D) full compressible Navier-Stokes equations on a half line $\mathbb{R}_+$. Instead of the classical…
In the present study, a characteristic-based boundary condition scheme is developed for the compressible magnetohydrodynamic (MHD) equations in the general curvilinear coordinate system, which is an extension of the characteristic boundary…
For a compact group G, we give a sufficient condition for embedding one G-equivariant vector bundle into another one and for a stable isomorphism between two such bundles to imply an isomorphism. Our criteria involve multiplicities of…
Typical multispecies compressible Navier-Stokes computations employ conservative equations for mass fraction transport. Upwind discretisations of these governing equations produce spurious pressure oscillations at diffuse contact surfaces…
In this paper, we design high order accurate and stable finite difference schemes for the initial-boundary value problem, associated with the magnetic induction equation with resistivity. We use Summation-By-Parts (SBP) finite difference…
The increasing use of deep neural networks for safety-critical applications, such as autonomous driving and flight control, raises concerns about their safety and reliability. Formal verification can address these concerns by guaranteeing…
We build a simple and general class of finite difference schemes for first order Hamilton-Jacobi (HJ) Partial Differential Equations. These filtered schemes are convergent to the unique viscosity solution of the equation. The schemes are…
Under compressive creep, visco-plastic solids experiencing internal mass transfer processes have been recently proposed to accommodate singular cnoidal wave solutions, as material instabilities at the stationary wave limit. These…