A Free-Lagrange method for unsteady compressible flow: simulation of a confined cylindrical blast wave |
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Authors: | G J Ball |
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Institution: | (1) Department of Aeronautics and Astronautics, University of Southampton, Southampton SO17 1BJ, UK , GB |
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Abstract: | A Free-Lagrange numerical procedure for the
simulation of two-dimensional inviscid compressible flow
is described in detail. The
unsteady Euler equations are solved on an unstructured
Lagrangian grid based on a density-weighted Voronoi mesh.
The flow solver is of the Godunov type, utilising either the
HLLE (2 wave) approximate Riemann solver or the more recent HLLC
(3 wave) variant, each adapted to the Lagrangian frame.
Within each mesh cell, conserved properties are
treated as piece-wise linear, and a slope limiter of the MUSCL type
is used to
give non-oscillatory behaviour with nominal
second order accuracy in space.
The solver is first order accurate in time.
Modifications to the slope limiter to minimise
grid and coordinate dependent
effects are described.
The performances of the HLLE and HLLC solvers are compared for
two test problems; a one-dimensional
shock tube and a two-dimensional blast wave confined
within a rigid cylinder. The blast wave is initiated by impulsive
heating of a gas column whose centreline is parallel to,
and one half of the cylinder radius from,
the axis of the cylinder.
For the shock tube problem, both solvers predict shock and expansion
waves in good agreement with theory.
For the HLLE solver, contact resolution
is poor, especially in the blast wave problem. The HLLC solver achieves
near-exact contact capture in both problems.
Received May 25, 1995 / Accepted September 11, 1995 |
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Keywords: | :Blast wave Contact surface Free-Lagrange scheme Riemann solver Shock focussing Voronoi mesh |
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