Search results for "compressible"
showing 10 items of 29 documents
Implicit-explicit and explicit projection schemes for the unsteady incompressible Navier–Stokes equations using a high-order dG method
2017
Abstract A modified version of the projection scheme [19] is proposed, which does not show a lower limit for the time step in contrast to the limits of stability observed numerically for some projection type schemes. An advantage of the proposed scheme is that the right-hand side of the Poisson equation for the pressure is independent of the time step. An explicit version of the current scheme is also provided besides the implicit-explicit one. For the implicit-explicit version, we retain divergence of the viscous terms on the right-hand side of the Poisson equation in order to achieve a higher accuracy for low Reynolds number flows. In this way, we also ensure that the Poisson equation wit…
Localized forms of the LBB condition and a posteriori estimates for incompressible media problems
2018
Abstract The inf–sup (or LBB) condition plays a crucial role in analysis of viscous flow problems and other problems related to incompressible media. In this paper, we deduce localized forms of this condition that contain a collection of local constants associated with subdomains instead of one global constant for the whole domain. Localized forms of the LBB inequality imply estimates of the distance to the set of divergence free fields. We use them and deduce fully computable bounds of the distance between approximate and exact solutions of boundary value problems arising in the theory of viscous incompressible fluids. The estimates are valid for approximations, which satisfy the incompres…
Inflow/outflow pressure boundary conditions for smoothed particle hydrodynamics simulations of incompressible flows
2017
Abstract Open Boundary treatment is a well-known issue in the Smoothed Particle Hydrodynamics (SPH) method, mainly when the truly Incompressible (ISPH) approach is employed. In the paper a novel method is proposed to set pressure boundary conditions in the computational domain inlets and outlets, without requiring the velocity profile assignment. The new technique allows to treat in the same way inflow and outflow sections, effectively dealing with the release of new particles at inlets and the deactivation of the ones leaving the domain through the outlets. Several 3D numerical tests, both in the laminar and turbulent regimes, are carried out to validate the proposed numerical scheme consi…
MAST-RT0 solution of the incompressible Navier–Stokes equations in 3D complex domains
2020
A new numerical methodology to solve the 3D Navier-Stokes equations for incompressible fluids within complex boundaries and unstructured body-fitted tetrahedral mesh is presented and validated with three literature and one real-case tests. We apply a fractional time step procedure where a predictor and a corrector problem are sequentially solved. The predictor step is solved applying the MAST (Marching in Space and Time) procedure, which explicitly handles the non-linear terms in the momentum equations, allowing numerical stability for Courant number greater than one. Correction steps are solved by a Mixed Hybrid Finite Elements discretization that assumes positive distances among tetrahedr…
Long time behavior for a dissipative shallow water model
2013
We consider the two-dimensional shallow water model derived by Levermore and Sammartino (Nonlinearity 14,2001), describing the motion of an incompressible fluid, confined in a shallow basin, with varying bottom topography. We construct the approximate inertial manifolds for the associated dynamical system and estimate its order. Finally, considering the whole domain R^2 and under suitable conditions on the time dependent forcing term, we prove the L^2 asymptotic decay of the weak solutions.
Compressibility and structural stability of ultra-incompressible bimetallic interstitial carbides and nitrides
2012
We have investigated by means of high-pressure x-ray diffraction the structural stability of Pd 2Mo 3N, Ni 2Mo 3C 0.52N 0.48, Co 3Mo 3C 0.62N 0.38, and Fe 3Mo 3C. We have found that they remain stable in their ambient-pressure cubic phase at least up to 48 GPa. All of them have a bulk modulus larger than 330 GPa, the least compressible material being Fe 3Mo 3C, B 0 = 374(3) GPa. In addition, apparently a reduction of compressibility is detected as the carbon content is increased. The equation of state for each material is determined. A comparison with other refractory materials indicates that interstitial nitrides and carbides behave as ultra-incompressible materials. © 2012 American Physic…
A Formal Passage From a System of Boltzmann Equations for Mixtures Towards a Vlasov-Euler System of Compressible Fluids
2019
A formal asymptotics leading from a system of Boltzmann equations for mixtures towards either Vlasov-Navier-Stokes or Vlasov-Stokes equations of incompressible fluids was established by the same authors and Etienne Bernard in: A Derivation of the Vlasov-Navier-Stokes Model for Aerosol Flows from Kinetic Theory Commun. Math. Sci., 15: 1703–1741 (2017) and A Derivation of the Vlasov-Stokes System for Aerosol Flows from the Kinetic Theory of Binary Gas Mixtures. KRM, 11: 43–69 (2018). With the same starting point but with a different scaling, we establish here a formal asymptotics leading to the Vlasov-Euler system of compressible fluids. Explicit formulas for the coupling terms are obtained i…
A stabilized finite element method for particulate two-phase flow equations laminar isothermal flow
1997
A finite element method for the solution of particulate two-phase flows is presented. The governing system has the form of compressible Navier-Stokes equations with unknown pressure. Therefore, the proposed method must capture the main features of stabilized methods used for incompressible as well as for compressible Navier-Stokes equations. Solution of the resulting nonlinear algebraic system of equations is based on the linearization using Newton method in conjunction with Generalized Minimal Residual iterative solver and Incomplete LU preconditioning. The method has been tested for three test cases including venturi tube flow, flow over backward step and mixing of flows in t-junction.
Comparison between adaptive and uniform discontinuous Galerkin simulations in dry 2D bubble experiments
2013
Accepted by the Journal of Computational Physics Adaptive mesh refinement generally aims to increase computational efficiency without compromising the accuracy of the numerical solution. However it is an open question in which regions the spatial resolution can actually be coarsened without affecting the accuracy of the result. This question is investigated for a specific example of dry atmospheric convection, namely the simulation of warm air bubbles. For this purpose a novel numerical model is developed that is tailored towards this specific application. The compressible Euler equations are solved with a Discontinuous Galerkin method. Time integration is done with an IMEXmethod and the dy…
Transition to turbulence in toroidal pipes
2011
AbstractIncompressible flow in toroidal pipes of circular cross-section was investigated by three-dimensional, time-dependent numerical simulations using a finite volume method. The computational domain included a whole torus and was discretized by up to ${\ensuremath{\sim} }11. 4\ensuremath{\times} 1{0}^{6} $ nodes. Two curvatures $\delta $ (radius of the cross-section/radius of the torus), namely 0.3 and 0.1, were examined; a streamwise forcing term was imposed, and its magnitude was made to vary so that the bulk Reynolds number ranged between ${\ensuremath{\sim} }3500$ and ${\ensuremath{\sim} }14\hspace{0.167em} 700$. The results were processed by different techniques in order to confirm…