633 research outputs found
An adaptive Cartesian embedded boundary approach for fluid simulations of two- and three-dimensional low temperature plasma filaments in complex geometries
We review a scalable two- and three-dimensional computer code for
low-temperature plasma simulations in multi-material complex geometries. Our
approach is based on embedded boundary (EB) finite volume discretizations of
the minimal fluid-plasma model on adaptive Cartesian grids, extended to also
account for charging of insulating surfaces. We discuss the spatial and
temporal discretization methods, and show that the resulting overall method is
second order convergent, monotone, and conservative (for smooth solutions).
Weak scalability with parallel efficiencies over 70\% are demonstrated up to
8192 cores and more than one billion cells. We then demonstrate the use of
adaptive mesh refinement in multiple two- and three-dimensional simulation
examples at modest cores counts. The examples include two-dimensional
simulations of surface streamers along insulators with surface roughness; fully
three-dimensional simulations of filaments in experimentally realizable
pin-plane geometries, and three-dimensional simulations of positive plasma
discharges in multi-material complex geometries. The largest computational
example uses up to million mesh cells with billions of unknowns on
computing cores. Our use of computer-aided design (CAD) and constructive solid
geometry (CSG) combined with capabilities for parallel computing offers
possibilities for performing three-dimensional transient plasma-fluid
simulations, also in multi-material complex geometries at moderate pressures
and comparatively large scale.Comment: 40 pages, 21 figure
Boundary Treatment and Multigrid Preconditioning for Semi-Lagrangian Schemes Applied to Hamilton-Jacobi-Bellman Equations
We analyse two practical aspects that arise in the numerical solution of
Hamilton-Jacobi-Bellman (HJB) equations by a particular class of monotone
approximation schemes known as semi-Lagrangian schemes. These schemes make use
of a wide stencil to achieve convergence and result in discretization matrices
that are less sparse and less local than those coming from standard finite
difference schemes. This leads to computational difficulties not encountered
there. In particular, we consider the overstepping of the domain boundary and
analyse the accuracy and stability of stencil truncation. This truncation
imposes a stricter CFL condition for explicit schemes in the vicinity of
boundaries than in the interior, such that implicit schemes become attractive.
We then study the use of geometric, algebraic and aggregation-based multigrid
preconditioners to solve the resulting discretised systems from implicit time
stepping schemes efficiently. Finally, we illustrate the performance of these
techniques numerically for benchmark test cases from the literature
A steady separated viscous corner flow
An example is presented of a separated flow in an unbounded domain in which, as the Reynolds number becomes large, the separated region remains of size 0(1) and tends to a non-trivial Prandtl-Batchelor flow. The multigrid method is used to obtain rapid convergence to the solution of the discretized Navier-Stokes equations at Reynolds numbers of up to 5000. Extremely fine grids and tests of an integral property of the flow ensure accuracy. The flow exhibits the separation of a boundary layer with ensuing formation of a downstream eddy and reattachment of a free shear layer. The asymptotic (’triple deck’) theory of laminar separation from a leading edge, due to Sychev (1979), is clarified and compared to the numerical solutions. Much better qualitative agreement is obtained than has been reported previously. Together with a plausible choice of two free parameters, the data can be extrapolated to infinite Reynolds number, giving quantitative agreement with triple-deck theory with errors of 20% or less. The development of a region of constant vorticity is observed in the downstream eddy, and the global infinite-Reynolds-number limit is a Prandtl-Batchelor flow; however, when the plate is stationary, the occurrence of secondary separation suggests that the limiting flow contains an infinite sequence of eddies behind the separation point. Secondary separation can be averted by driving the plate, and in this case the limit is a single-vortex Prandtl-Batchelor flow of the type found by Moore, Saffman & Tanveer (1988); detailed, encouraging comparisons are made to the vortex-sheet strength and position. Altering the boundary condition on the plate gives viscous eddies that approximate different members of the family of inviscid solutions
Parallel numerical modeling of hybrid-dimensional compositional non-isothermal Darcy flows in fractured porous media
This paper introduces a new discrete fracture model accounting for
non-isothermal compositional multiphase Darcy flows and complex networks of
fractures with intersecting, immersed and non immersed fractures. The so called
hybrid-dimensional model using a 2D model in the fractures coupled with a 3D
model in the matrix is first derived rigorously starting from the
equi-dimensional matrix fracture model. Then, it is dis-cretized using a fully
implicit time integration combined with the Vertex Approximate Gradient (VAG)
finite volume scheme which is adapted to polyhedral meshes and anisotropic
heterogeneous media. The fully coupled systems are assembled and solved in
parallel using the Single Program Multiple Data (SPMD) paradigm with one layer
of ghost cells. This strategy allows for a local assembly of the discrete
systems. An efficient preconditioner is implemented to solve the linear systems
at each time step and each Newton type iteration of the simulation. The
numerical efficiency of our approach is assessed on different meshes, fracture
networks, and physical settings in terms of parallel scalability, nonlinear
convergence and linear convergence
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