Recent Advances in Adaptive Computation

The ability to handle complex geometries is an important part of transient calculations; therefore, the need for fully automatic mesh generation capable of dealing with general geometries is quite demanded. In this paper a specific approach to fully automatic three-dimensional mesh generation is presented. An approach of moving the generated mesh is also outlined. Particularly, the simulation of a diesel injector needle movement is sought. The movement of the needle in the moving meshes calculations based on injection rate experimental data and injection rate predicted data with steady state boundaries and geometry. The simulation performed with the commercial code STAR-CD version 4.06.

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A moving mesh generation strategy for solving an injector internal flow problem

Margot

Hoyas

Fajardo

et al. 2010

Mathematical and Computer Modelling

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Moving mesh partial differential equations modelling to describe oxygen induced effects on avascular tumour growth

Amoddeo

2015

Cogent Physics

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Space–time adaptive numerical methods for geophysical applications

Castro

Käser

Toro

2009

Phil. Trans. R. Soc. A.

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In this paper we present high-order formulations of the finite volume and discontinuous Galerkin finite-element methods for wave propagation problems with a space-time adaptation technique using unstructured meshes in order to reduce computational cost without reducing accuracy. Both methods can be derived in a similar mathematical framework and are identical in their first-order version. In their extension to higher order accuracy in space and time, both methods use spatial polynomials of higher degree inside each element, a high-order solution of the generalized Riemann problem and a high-order time integration method based on the Taylor series expansion. The static adaptation strategy uses locally refined high-resolution meshes in areas with low wave speeds to improve the approximation quality. Furthermore, the time step length is chosen locally adaptive such that the solution is evolved explicitly in time by an optimal time step determined by a local stability criterion. After validating the numerical approach, both schemes are applied to geophysical wave propagation problems such as tsunami waves and seismic waves comparing the new approach with the classical global timestepping technique. The problem of mesh partitioning for large-scale applications on multi-processor architectures is discussed and a new mesh partition approach is proposed and tested to further reduce computational cost.

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Recent Advances in Adaptive Computation

Cited by 4 publications

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A moving mesh generation strategy for solving an injector internal flow problem

A moving mesh generation strategy for solving an injector internal flow problem

Moving mesh partial differential equations modelling to describe oxygen induced effects on avascular tumour growth

Space–time adaptive numerical methods for geophysical applications

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