27 research outputs found
Constraint-preserving boundary conditions in the 3+1 first-order approach
A set of energy-momentum constraint-preserving boundary conditions is
proposed for the first-order Z4 case. The stability of a simple numerical
implementation is tested in the linear regime (robust stability test), both
with the standard corner and vertex treatment and with a modified
finite-differences stencil for boundary points which avoids corners and
vertices even in cartesian-like grids. Moreover, the proposed boundary
conditions are tested in a strong field scenario, the Gowdy waves metric,
showing the expected rate of convergence. The accumulated amount of
energy-momentum constraint violations is similar or even smaller than the one
generated by either periodic or reflection conditions, which are exact in the
Gowdy waves case. As a side theoretical result, a new symmetrizer is explicitly
given, which extends the parametric domain of symmetric hyperbolicity for the
Z4 formalism. The application of these results to first-order BSSN-like
formalisms is also considered.Comment: Revised version, with conclusive numerical evidence. 23 pages, 12
figure
Towards a gauge-polyvalent Numerical Relativity code
The gauge polyvalence of a new numerical code is tested, both in
harmonic-coordinate simulations (gauge-waves testbed) and in
singularity-avoiding coordinates (simple Black-Hole simulations, either with or
without shift). The code is built upon an adjusted first-order
flux-conservative version of the Z4 formalism and a recently proposed family of
robust finite-difference high-resolution algorithms. An outstanding result is
the long-term evolution (up to 1000M) of a Black-Hole in normal coordinates
(zero shift) without excision.Comment: to appear in Physical Review
Geometrically motivated hyperbolic coordinate conditions for numerical relativity: Analysis, issues and implementations
We study the implications of adopting hyperbolic driver coordinate conditions
motivated by geometrical considerations. In particular, conditions that
minimize the rate of change of the metric variables. We analyze the properties
of the resulting system of equations and their effect when implementing
excision techniques. We find that commonly used coordinate conditions lead to a
characteristic structure at the excision surface where some modes are not of
outflow-type with respect to any excision boundary chosen inside the horizon.
Thus, boundary conditions are required for these modes. Unfortunately, the
specification of these conditions is a delicate issue as the outflow modes
involve both gauge and main variables. As an alternative to these driver
equations, we examine conditions derived from extremizing a scalar constructed
from Killing's equation and present specific numerical examples.Comment: 9 figure
Efficient implementation of finite volume methods in Numerical Relativity
Centered finite volume methods are considered in the context of Numerical
Relativity. A specific formulation is presented, in which third-order space
accuracy is reached by using a piecewise-linear reconstruction. This
formulation can be interpreted as an 'adaptive viscosity' modification of
centered finite difference algorithms. These points are fully confirmed by 1D
black-hole simulations. In the 3D case, evidence is found that the use of a
conformal decomposition is a key ingredient for the robustness of black hole
numerical codes.Comment: Revised version, 10 pages, 6 figures. To appear in Phys. Rev.
Lattice Boltzmann - Langevin simulations of binary mixtures
We report a hybrid numerical method for the solution of the model H
fluctuating hydrodynamic equations for binary mixtures. The momentum
conservation equations with Landau-Lifshitz stresses are solved using the
fluctuating lattice Boltzmann equation while the order parameter conservation
equation with Langevin fluxes are solved using the stochastic method of lines.
Two methods, based on finite difference and finite volume, are proposed for
spatial discretisation of the order parameter equation. Special care is taken
to ensure that the fluctuation-dissipation theorem is maintained at the lattice
level in both cases. The methods are benchmarked by comparing static and
dynamic correlations and excellent agreement is found between analytical and
numerical results. The Galilean invariance of the model is tested and found to
be satisfactory. Thermally induced capillary fluctuations of the interface are
captured accurately, indicating that the model can be used to study nonlinear
fluctuations