724 research outputs found
Local time steps for a finite volume scheme
We present a strategy for solving time-dependent problems on grids with local
refinements in time using different time steps in different regions of space.
We discuss and analyze two conservative approximations based on finite volume
with piecewise constant projections and domain decomposition techniques. Next
we present an iterative method for solving the composite-grid system that
reduces to solution of standard problems with standard time stepping on the
coarse and fine grids. At every step of the algorithm, conservativity is
ensured. Finally, numerical results illustrate the accuracy of the proposed
methods
High performance computing of explicit schemes for electrofusion jointing process based on message-passing paradigm
The research focused on heterogeneous cluster workstations comprising of a number of CPUs in single and shared architecture platform. The problem statements under consideration involved one dimensional parabolic equations. The thermal process of electrofusion jointing was also discussed. Numerical schemes of explicit type such as AGE, Brian, and Charlies Methods were employed. The parallelization of these methods were based on the domain decomposition technique. Some parallel performance measurement for these methods were also addressed. Temperature profile of the one dimensional radial model of the electrofusion process were also given
Multirate Timestepping for the Incompressible Navier-Stokes Equations in Overlapping Grids
We develop a multirate timestepper for semi-implicit solutions of the
unsteady incompressible Navier-Stokes equations (INSE) based on a
recently-developed multidomain spectral element method (SEM). For {\em
incompressible} flows, multirate timestepping (MTS) is particularly challenging
because of the tight coupling implied by the incompressibility constraint,
which manifests as an elliptic subproblem for the pressure at each timestep.
The novelty of our approach stems from the development of a stable overlapping
Schwarz method applied directly to the Navier-Stokes equations, rather than to
the convective, viscous, and pressure substeps that are at the heart of most
INSE solvers. Our MTS approach is based on a predictor-corrector (PC) strategy
that preserves the temporal convergence of the underlying semi-implicit
timestepper. We present numerical results demonstrating that this approach
scales to an arbitrary number of overlapping grids, accurately models complex
turbulent flow phenomenon, and improves computational efficiency in comparison
to singlerate timestepping-based calculations.Comment: 40 pages, 13 figure
Numerical analysis of conservative unstructured discretisations for low Mach flows
This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving. https://authorservices.wiley.com/author-resources/Journal-Authors/licensing-and-open-access/open-access/self-archiving.htmlUnstructured meshes allow easily representing complex geometries and to refine in regions of interest without adding control volumes in unnecessary regions.
However, numerical schemes used on unstructured grids have to be properly defined in order to minimise numerical errors.
An assessment of a low-Mach algorithm for laminar and turbulent flows on unstructured meshes using collocated and staggered formulations is presented. For staggered formulations using cell centred velocity reconstructions the standard first-order method is shown to be inaccurate in low Mach flows on unstructured grids. A recently proposed least squares procedure for incompressible flows is extended to the low Mach regime and shown to significantly improve the behaviour of the algorithm.
Regarding collocated discretisations, the odd-even pressure decoupling is handled through a kinetic energy conserving flux interpolation scheme. This approach is shown to efficiently handle variable-density flows.
Besides, different face interpolations schemes for unstructured meshes are analysed.
A kinetic energy preserving scheme is applied to the momentum equations, namely the Symmetry-Preserving (SP) scheme. Furthermore, a new approach to define the far-neighbouring nodes of the QUICK scheme is presented and analysed. The method is suitable for both structured and unstructured grids, either uniform or not.
The proposed algorithm and the spatial schemes are assessed against a function reconstruction, a differentially heated cavity and a turbulent self-igniting diffusion flame. It is shown that the proposed algorithm accurately represents unsteady variable-density flows. Furthermore, the QUICK schemes shows close to second order behaviour on unstructured meshes and the SP is reliably used in all computations.Peer ReviewedPostprint (author's final draft
Arbitrary-Lagrangian-Eulerian discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes
We present a new family of high order accurate fully discrete one-step
Discontinuous Galerkin (DG) finite element schemes on moving unstructured
meshes for the solution of nonlinear hyperbolic PDE in multiple space
dimensions, which may also include parabolic terms in order to model
dissipative transport processes. High order piecewise polynomials are adopted
to represent the discrete solution at each time level and within each spatial
control volume of the computational grid, while high order of accuracy in time
is achieved by the ADER approach. In our algorithm the spatial mesh
configuration can be defined in two different ways: either by an isoparametric
approach that generates curved control volumes, or by a piecewise linear
decomposition of each spatial control volume into simplex sub-elements. Our
numerical method belongs to the category of direct
Arbitrary-Lagrangian-Eulerian (ALE) schemes, where a space-time conservation
formulation of the governing PDE system is considered and which already takes
into account the new grid geometry directly during the computation of the
numerical fluxes. Our new Lagrangian-type DG scheme adopts the novel a
posteriori sub-cell finite volume limiter method, in which the validity of the
candidate solution produced in each cell by an unlimited ADER-DG scheme is
verified against a set of physical and numerical detection criteria. Those
cells which do not satisfy all of the above criteria are flagged as troubled
cells and are recomputed with a second order TVD finite volume scheme. The
numerical convergence rates of the new ALE ADER-DG schemes are studied up to
fourth order in space and time and several test problems are simulated.
Finally, an application inspired by Inertial Confinement Fusion (ICF) type
flows is considered by solving the Euler equations and the PDE of viscous and
resistive magnetohydrodynamics (VRMHD).Comment: 39 pages, 21 figure
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