589 research outputs found
ADER-WENO Finite Volume Schemes with Space-Time Adaptive Mesh Refinement
We present the first high order one-step ADER-WENO finite volume scheme with
Adaptive Mesh Refinement (AMR) in multiple space dimensions. High order spatial
accuracy is obtained through a WENO reconstruction, while a high order one-step
time discretization is achieved using a local space-time discontinuous Galerkin
predictor method. Due to the one-step nature of the underlying scheme, the
resulting algorithm is particularly well suited for an AMR strategy on
space-time adaptive meshes, i.e.with time-accurate local time stepping. The AMR
property has been implemented 'cell-by-cell', with a standard tree-type
algorithm, while the scheme has been parallelized via the Message Passing
Interface (MPI) paradigm. The new scheme has been tested over a wide range of
examples for nonlinear systems of hyperbolic conservation laws, including the
classical Euler equations of compressible gas dynamics and the equations of
magnetohydrodynamics (MHD). High order in space and time have been confirmed
via a numerical convergence study and a detailed analysis of the computational
speed-up with respect to highly refined uniform meshes is also presented. We
also show test problems where the presented high order AMR scheme behaves
clearly better than traditional second order AMR methods. The proposed scheme
that combines for the first time high order ADER methods with space--time
adaptive grids in two and three space dimensions is likely to become a useful
tool in several fields of computational physics, applied mathematics and
mechanics.Comment: With updated bibliography informatio
RAM: A Relativistic Adaptive Mesh Refinement Hydrodynamics Code
We have developed a new computer code, RAM, to solve the conservative
equations of special relativistic hydrodynamics (SRHD) using adaptive mesh
refinement (AMR) on parallel computers. We have implemented a
characteristic-wise, finite difference, weighted essentially non-oscillatory
(WENO) scheme using the full characteristic decomposition of the SRHD equations
to achieve fifth-order accuracy in space. For time integration we use the
method of lines with a third-order total variation diminishing (TVD)
Runge-Kutta scheme. We have also implemented fourth and fifth order Runge-Kutta
time integration schemes for comparison. The implementation of AMR and
parallelization is based on the FLASH code. RAM is modular and includes the
capability to easily swap hydrodynamics solvers, reconstruction methods and
physics modules. In addition to WENO we have implemented a finite volume module
with the piecewise parabolic method (PPM) for reconstruction and the modified
Marquina approximate Riemann solver to work with TVD Runge-Kutta time
integration. We examine the difficulty of accurately simulating shear flows in
numerical relativistic hydrodynamics codes. We show that under-resolved
simulations of simple test problems with transverse velocity components produce
incorrect results and demonstrate the ability of RAM to correctly solve these
problems. RAM has been tested in one, two and three dimensions and in
Cartesian, cylindrical and spherical coordinates. We have demonstrated
fifth-order accuracy for WENO in one and two dimensions and performed detailed
comparison with other schemes for which we show significantly lower convergence
rates. Extensive testing is presented demonstrating the ability of RAM to
address challenging open questions in relativistic astrophysics.Comment: ApJS in press, 21 pages including 18 figures (6 color figures
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