Narrow Results

Recently, Halliday et al. presented an idea by inserting the "source" terms into the two-dimensional (2D) lattice Boltzmann equation (LBE) so that the emergent dynamics of the lattice fluid can be transformed into the cylindrical polar system. This paper further extends the idea of Halliday et al. to include the effect of azimuthal rotation. The terms related to the azimuthal effect are considered as inertia forces. By using our recently developed Taylor-series-expansion and least-square-based lattice Boltzmann method (TLLBM) for the transformed LBE and a second order explicit finite difference method for the azimuthal moment equation, Taylor–Couette flows between two concentric cylinders with the inner cylinder rotating were simulated. To show the performance of the proposed model, the same problem was also simulated by the three-dimensional (3D) LBM. Numerical results showed that the present axisymmetric model is much more efficient than the 3D model for an axisymmetric flow problem.

We find a wide variety of exact classical solutions to Yang–Mills–Chern–Simons theory coupled to an external source, ranging periodic ones to localised soliton type. The solutions are found by choosing an ansatz, which reduces the classical equation of motion to a set of coupled non-linear ordinary differential equations, which are then solved. It is seen that these classical solutions necessarily exist over a non-zero background field whose intensity is controlled by external source strength.

In the low energy part of an ion accelerator, the ion beam reaches the first accelerating device through a drift tube where a residual neutral gas is present. A process of ionization takes place and secondary electrons and ions are created. We analyze the coupling between these secondary particles, the beam density and the electrical potential.

In a previous article,² we proved that a stationary Vlasov–Poisson problem with ionization source terms, which, at first sight, seems the natural model for this system, does not admit solutions. To overcome this difficulty, we propose here a heuristic model which consists of modifying the electron source term. In this new frame, we prove that the problem can be solved and we give numerical examples.

Well-balanced or asymptotic preserving schemes are receiving an increasing amount of interest. This paper gives a precise setting for studying both properties in the case of Euler system with friction. We derive a simple solver which, by construction, preserves discrete equilibria and reproduces at the discrete level the same asymptotic behavior as that of the solutions of the continuous system. Numerical illustrations are convincing and show that not all methods share these properties.

This paper is devoted to possibilities of a semi-analytical approximation of nonlinear wave equations with nonlinearities depending on the absolute value of the unknown function, which arise in different areas of physics and mechanics. The main difficulty of analysis of such equations is that the derivation of their rigorous solution is highly sophisticated, while their numerical solution requires burdensome computational costs. Using the traveling wave ansatz, we first reduce the wave equation to a nonlinear ordinary differential equation. Then, applying Frasca’s method, we construct its general solution in terms of the nonlinear Green’s function. For particular nonlinearities, it is shown that the first-order approximation of the Green’s function solution is numerically comparable with the solution obtained by the well-known numerical method of lines. The contribution of the higher order terms is studied for a particular nonlinearity.

We propose and prove convergence of a front tracking method for scalar conservation laws with source term. The method is based on writing the single conservation law as a 2×2 quasilinear system without a source term, and employ the solution of the Riemann problem for this system in the front tracking procedure. In this way the source term is processed in the Riemann solver, and one avoids using operator splitting. Since we want to treat the resonant regime, classical arguments for bounding the total variation of numerical solutions do not apply here. Instead compactness of a sequence of front tracking solutions is achieved using a variant of the singular mapping technique invented by Temple [69]. The front tracking method has no CFL-condition associated with it, and it does not discriminate between stiff and non-stiff source terms. This makes it an attractive approach for stiff problems, as is demonstrated in numerical examples. In addition, the numerical examples show that the front tracking method is able to preserve steady-state solutions (or achieving them in the long time limit) with good accuracy.

A methodology applying the Laplaces transformation to the solution of particular systems of Ordinary Differential Equations (ODEs) is presented that can be used in the calculation of inventory of radioactive nuclides and fission products in the core of a nuclear power reactor. A number of simplifying assumptions regarding fission products generation by thermal and fast fission of Uranium and Plutonium isotopes are introduced, but a detailed description of the decay process, including branching of decay chains, is used. The proposed mathematical modeling is indeed general and could be applied to other classes of problem involving the solution of systems of chained ODEs.