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We consider different inner boundary conditions for BHs and NSs: outflow boundary condition mimicking mass sink at the centre valid for BHs; and reflective and steady-shock allowing gas to cross the inner boundary at subsonic speeds boundary conditions for NSs.

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We also obtain a similarity solution for cold accretion on to BHs and NSs. Entropy is the highest at the bottom of the subsonic region for reflective boundary conditions. In 2D this profile is convectively unstable. Using steady-shock inner boundary conditions, the flow is unstable to the standing accretion shock instability in 2D, which leads to global shock oscillations and may be responsible for quasi-periodic oscillations seen in the light curves of accreting systems.

For steady accretion in the quiescent state, spherical accretion rate on to an NS can be suppressed by orders of magnitude compared to that on to a BH. Oxford University Press is a department of the University of Oxford.

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Spherical accretion: the influence of inner boundary and quasi-periodic oscillations Prasun Dhang. Oxford Academic. Google Scholar. The added point numbers must be the ones returned from mesh.

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Add MeshPoint. This is a manually created mesh with periodic boundaries:. The periodic finite element space is created using the generator function Periodic. A quasi-periodic space can be created the same way if the optional parameter 'phase' is set. The phase shifts must be given in the same order as the definition of the periodic boundaries in the geometry!

Since the dofs are mapped to the other side, periodic spaces are not possible on meshes with only one element in the direction of the periodic boundaries then the elementmatrix would need to be of different size and NGSolve cannot handle that. So make sure that the meshsize is less than half your domain width! You can download these examples here: 1D , 2D , 3D. Periodic or quasi-periodic Finite Element Spaces. The periodic fespace is a wrapper around a standard fespace with an additional dof mapping for the periodic degrees of freedom. All dofs on slave boundaries are mapped to their master dofs. Because of this, the mesh needs to be periodic. Low order fespaces are currently not supported, so methods using them will not work. The basis functions on the slave boundary are multiplied by the factor given in this list. If None default is given, a periodic fespace is created. The order of the list must match the order of the definition of the periodic boundaries in the mesh. Regular expression string defining the dirichlet boundary. More than one boundary can be combined by the operator, i.

FESpace is only defined on specific Region, created with mesh.

Materials 'regexpr' or mesh. Boundaries 'regexpr'. If given a regexpr, the region is assumed to be mesh. Materials 'regexpr'.

Introduction and main result

Enable discontinuous space for DG methods, this flag is needed for DG methods, since the dofs have a different coupling then and this changes the sparsity pattern of matrices. Generate a lowest order space together with the high-order space, needed for some preconditioners. NGS-Py 6.