Related papers: A Bicharacteristic Scheme for the Numerical Comput…
We describe a Continuous Hugoniot Method for the efficient simulation of shock wave fronts. This approach achieves significantly improved efficiency when the generation of a tightly spaced collection of individual steady-state shock front…
We experimentally study quasi-2d dilute granular flow around intruders whose shape, size and relative impact speed are systematically varied. Direct measurement of the flow field reveals that three in-principle independent measurements of…
Low-frequency molecular fluctuations in the translational nonequilibrium zone of one-dimensional strong shock waves are characterised for the first time in a kinetic collisional framework in the Mach number range $2\le M\le 10$. Our…
Godunov type numerical schemes for the class of hyperbolic systems, admitting non-classical $\delta-$ shocks are proposed. It is shown that the numerical approximations converge to the solution and preserve the physical properties of the…
A new scheme that tightly couples kinetic turbulence codes across a spatial interface is introduced. This scheme evolves from considerations of competing strategies and down-selection. It is found that the use of a composite kinetic…
In this article we develop a numerical scheme to deal with interfaces between touching numerical grids when solving the second-order wave equation. We show that it is possible to implement an interface scheme of "penalty" type for the…
We present a rigorous mathematical analysis of the modeling of inviscid water waves. The free-surface is described as a parametrized curve. We introduce a numerically stable algorithm which accounts for its evolution with time. The method…
We present a high-resolution convergence study of detonation initiated by a temperature gradient in a stoichiometric hydrogen-oxygen mixture using the Pencil Code and compare with a code that employs a fifth order weighted essentially…
This paper concerns the dynamic stability of the steady 3-D wave structure of a planar normal shock front intersecting perpendicularly to a planar solid wall for unsteady potential flows. The stability problem can be formulated as a free…
We propose a fully discretised numerical scheme for the hyperelastic rod wave equation on the line. The convergence of the method is established. Moreover, the scheme can handle the blow-up of the derivative which naturally occurs for this…
We extensively investigate two-step shape invariance in the framework of N-fold supersymmetry. We first show that any two-step shape-invariant system possesses type A 2-fold supersymmetry with an intermediate Hamiltonian and thus has…
In this paper, a parameter-uniform fitted mesh finite difference scheme is constructed and analyzed for a class of singularly perturbed interior turning point problems. The solution of this class of turning point problem possess two outflow…
An approach for quantitatively evaluating overshooting oscillations is designed to characterize the performance of shock-capturing schemes. Specifically, following our previous work focused on cases with only discontinuities, now we account…
We introduce a new approach for designing numerical schemes for stochastic differential equations (SDEs). The approach, which we have called direction and norm decomposition method, proposes to approximate the required solution $X_t$ by…
We address a numerical instability that arises in the directionally split computation of hydrodynamic flows when shock fronts are parallel to a grid plane. Transverse oscillations in pressure, density and temperature are produced that are…
The paper proposes a method to characterize the bend discontinuity for plasmonic and spoof plasmonic waveguides in terms of scattering parameters. By means of this method, the waveguide is modelled by a two-port network and its scattering…
Mathematical methods of step-by-step and combined shifts are proposed for experimental data processing to reconstruct the measuring system impulse response distorted by shift-invariant blur. Proposed methods base on direct non-blind…
We study the construction and convergence of decoupling multistep schemes of higher order using the backward differentiation formulae for an elliptic-parabolic problem, which includes multiple-network poroelasticity as a special case. These…
Integrable two-dimensional models which possess an integral of motion cubic or quartic in velocities are governed by a single prepotential, which obeys a nonlinear partial differential equation. Taking into account the latter's invariance…
In this paper, we develop the ball-approximated characteristics (B-char) method, which is an algorithm for efficiently implementing characteristic-based schemes in 2D and 3D. Core to the implementation of numerical schemes is the evaluation…