Related papers: Pade: A code for protoplanetary disk turbulence ba…
In this article, we have developed a higher order compact numerical method for variable coefficient parabolic problems with mixed derivatives. The finite difference scheme, presented here for two-dimensional domains, is based on fourth…
We present a new numerical code, PLUTO, for the solution of hypersonic flows in 1, 2 and 3 spatial dimensions and different systems of coordinates. The code provides a multi-physics, multi-algorithm modular environment particularly oriented…
Explicit Runge-Kutta schemes with large stable step sizes are developed for integration of high order spectral difference spatial discretization on quadrilateral grids. The new schemes permit an effective time step that is substantially…
We present a newly developed cosmological hydrodynamics code based on weighted essentially non-oscillatory (WENO) schemes for hyperbolic conservation laws. WENO is a higher order accurate finite difference scheme designed for problems with…
We propose novel less diffusive schemes for conservative one- and two-dimensional hyperbolic systems of nonlinear partial differential equations (PDEs). The main challenges in the development of accurate and robust numerical methods for the…
A general purpose, modular program package for the integration of large number of independent ordinary differential equation systems capable of using professional graphics cards is presented. The available numerical schemes are the explicit…
Proto-planetary discs, the birth environment of planets, are an example of a structure commonly found in astrophysics, accretion discs. Identifying the mechanism responsible for accretion is a long-standing problem, dating back several…
A cosmological multidimensional hydrodynamic code is described and tested. This code is based on modern high-resolution shock-capturing techniques. It can make use of a linear or a parabolic cell reconstruction as well as an approximate…
Transit timing variations - deviations from strict periodicity between successive passages of a transiting planet - can be used to probe the structure and dynamics of multiple-planet systems. In this paper, we examine prospects for…
Context: Calculating stellar pulsations requires a sufficient accuracy to match the quality of the observations. Many current pulsation codes apply a second order finite-difference scheme, combined with Richardson extrapolation to reach…
Warped accretion discs of low viscosity are prone to hydrodynamic instability due to parametric resonance of inertial waves as confirmed by local simulations. Global simulations of warped discs, using either smoothed particle hydrodynamics…
Purely dispersive partial differential equations as the Korteweg-de Vries equation, the nonlinear Schr\"odinger equation and higher dimensional generalizations thereof can have solutions which develop a zone of rapid modulated oscillations…
A nonlinear adaptive procedure for optimising both the schemes in time and space is proposed in view of increasing the numerical efficiency and reducing the computational time. The method is based on a four-parameter family of schemes we…
A computational fluid model is developed to study waves and instabilities. A new technique involving initial perturbations in configuration space have been implemented to excite the plasma waves; i.e. the perturbations acting similar to a…
Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential…
We present an efficient and simple modification of the standard transport algorithm used in explicit eulerian fixed polar grid codes, aimed at getting rid of the average azimuthal velocity when applying the Courant condition. This results…
A novel numerical approach to solving the shallow-water equations on the sphere using high-order numerical discretizations in both space and time is proposed. A space-time tensor formalism is used to express the equations of motion…
We consider a spherical variant of the Faraday problem, in which a spherical drop is subjected to a time-periodic body force, as well as surface tension. We use a full three-dimensional parallel front-tracking code to calculate the…
A linear evolving surface partial differential equation is first discretized in space by an arbitrary Lagrangian Eulerian (ALE) evolving surface finite element method, and then in time either by a Runge-Kutta method, or by a backward…
Accretion disc turbulence is investigated in the framework of the shearing box approximation. The turbulence is either driven by the magneto-rotational instability or, in the non-magnetic case, by an explicit and artificial forcing term in…