4,128 research outputs found
Low Mach number effect in simulation of high Mach number flow
In this note, we relate the two well-known difficulties of Godunov schemes:
the carbuncle phenomena in simulating high Mach number flow, and the inaccurate
pressure profile in simulating low Mach number flow. We introduced two simple
low-Mach-number modifications for the classical Roe flux to decrease the
difference between the acoustic and advection contributions of the numerical
dissipation. While the first modification increases the local numerical
dissipation, the second decreases it. The numerical tests on the double-Mach
reflection problem show that both modifications eliminate the kinked Mach stem
suffered by the original flux. These results suggest that, other than
insufficient numerical dissipation near the shock front, the carbuncle
phenomena is strongly relevant to the non-comparable acoustic and advection
contributions of the numerical dissipation produced by Godunov schemes due to
the low Mach number effect.Comment: 9 pages, 1 figur
Kinetic Solvers with Adaptive Mesh in Phase Space
An Adaptive Mesh in Phase Space (AMPS) methodology has been developed for
solving multi-dimensional kinetic equations by the discrete velocity method. A
Cartesian mesh for both configuration (r) and velocity (v) spaces is produced
using a tree of trees data structure. The mesh in r-space is automatically
generated around embedded boundaries and dynamically adapted to local solution
properties. The mesh in v-space is created on-the-fly for each cell in r-space.
Mappings between neighboring v-space trees implemented for the advection
operator in configuration space. We have developed new algorithms for solving
the full Boltzmann and linear Boltzmann equations with AMPS. Several recent
innovations were used to calculate the discrete Boltzmann collision integral
with dynamically adaptive mesh in velocity space: importance sampling,
multi-point projection method, and the variance reduction method. We have
developed an efficient algorithm for calculating the linear Boltzmann collision
integral for elastic and inelastic collisions in a Lorentz gas. New AMPS
technique has been demonstrated for simulations of hypersonic rarefied gas
flows, ion and electron kinetics in weakly ionized plasma, radiation and light
particle transport through thin films, and electron streaming in
semiconductors. We have shown that AMPS allows minimizing the number of cells
in phase space to reduce computational cost and memory usage for solving
challenging kinetic problems
A Level Set Approach to Eulerian-Lagrangian Coupling
We present a numerical method for coupling an Eulerian compressible flow solver with a Lagrangian solver for fast transient problems involving fluid-solid interactions. Such coupling needs arise when either specific solution methods or accuracy considerations necessitate that different
and disjoint subdomains be treated with different (Eulerian or Lagrangian)schemes.
The algorithm we propose employs standard integration of the Eulerian
solution over a Cartesian mesh. To treat the irregular boundary cells that
are generated by an arbitrary boundary on a structured grid, the Eulerian
computational domain is augmented by a thin layer of Cartesian ghost cells.
Boundary conditions at these cells are established by enforcing conservation
of mass and continuity of the stress tensor in the direction normal to the
boundary. The description and the kinematic constraints of the Eulerian
boundary rely on the unstructured Lagrangian mesh. The Lagrangian mesh
evolves concurrently, driven by the traction boundary conditions imposed
by the Eulerian counterpart.
Several numerical tests designed to measure the rate of convergence and
accuracy of the coupling algorithm are presented as well. General problems
in one and two dimensions are considered, including a test consisting of an
isotropic elastic solid and a compressible fluid in a fully coupled setting
where the exact solution is available
Multidimensional HLLE Riemann solver; Application to Euler and Magnetohydrodynamic Flows
In this work we present a general strategy for constructing multidimensional
Riemann solvers with a single intermediate state, with particular attention
paid to detailing the two-dimensional Riemann solver. This is accomplished by
introducing a constant resolved state between the states being considered,
which introduces sufficient dissipation for systems of conservation laws.
Closed form expressions for the resolved fluxes are also provided to facilitate
numerical implementation. The Riemann solver is proved to be positively
conservative for the density variable; the positivity of the pressure variable
has been demonstrated for Euler flows when the divergence in the fluid
velocities is suitably restricted so as to prevent the formation of cavitation
in the flow.
We also focus on the construction of multidimensionally upwinded electric
fields for divergence-free magnetohydrodynamical flows. A robust and efficient
second order accurate numerical scheme for two and three dimensional Euler and
magnetohydrodynamic flows is presented. The scheme is built on the current
multidimensional Riemann solver. The number of zones updated per second by this
scheme on a modern processor is shown to be cost competitive with schemes that
are based on a one-dimensional Riemann solver. However, the present scheme
permits larger timesteps
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