Search results for "Inviscid flow"
showing 6 items of 26 documents
A Second Order Accurate Kinetic Relaxation Scheme for Inviscid Compressible Flows
2013
In this paper we present a kinetic relaxation scheme for the Euler equations of gas dynamics in one space dimension. The method is easily applicable to solve any complex system of conservation laws. The numerical scheme is based on a relaxation approximation for conservation laws viewed as a discrete velocity model of the Boltzmann equation of kinetic theory. The discrete kinetic equation is solved by a splitting method consisting of a convection phase and a collision phase. The convection phase involves only the solution of linear transport equations and the collision phase instantaneously relaxes the distribution function to an equilibrium distribution. We prove that the first order accur…
BEM Formulation of the Trailing Edge Condition
1995
This paper deals with a BEM formulation of the trailing edge condition to determine the potential flow field around an airfoil. It is seen the trailing edge condition is not sufficient to give an unique solution. It is necessary to assign a further condition to eliminate the nonuniqueness of the solution. The approach allows to adopt a discretization into superior order elements. Some preliminary applications show the validity of the formulation.
Radiative Shocks in Rotating Accretion Flows around Black Holes
2004
It is well known that the rotating inviscid accretion flows with adequate injection parameters around black holes could form shock waves close to the black holes, after the flow passes through the outer sonic point and can be virtually stopped by the centrifugal force. We examine numerically such shock waves in 1D and 2D accretion flows, taking account of cooling and heating of the gas and radiation transport. The numerical results show that the shock location shifts outward compared with that in the adiabatic solutions and that the more rarefied ambient density leads to the more outward shock location. In the 2D-flow, we find an intermediate frequency QPO behavior of the shock location as …
On a rough perturbation of the Navier-Stokes system and its vorticity formulation
2019
We introduce a rough perturbation of the Navier-Stokes system and justify its physical relevance from balance of momentum and conservation of circulation in the inviscid limit. We present a framework for a well-posedness analysis of the system. In particular, we define an intrinsic notion of solution based on ideas from the rough path theory and study the system in an equivalent vorticity formulation. In two space dimensions, we prove that well-posedness and enstrophy balance holds. Moreover, we derive rough path continuity of the equation, which yields a Wong-Zakai result for Brownian driving paths, and show that for a large class of driving signals, the system generates a continuous rando…
A Unified Perspective on the Dynamics of Axisymmetric Hurricanes and Monsoons
2006
Abstract This paper provides a unified perspective on the dynamics of hurricane- and monsoonlike vortices by identifying them as specific limiting cases of a more general flow system. This more general system is defined as stationary axisymmetric balanced flow of a stably stratified non-Boussinesq atmosphere on the f plane. The model is based on the primitive equations assuming gradient wind balance in the radial momentum equation. The flow is forced by heating in the vortex center, which is implemented as relaxation toward a specified equilibrium temperature Te. The flow is dissipated through surface friction, and it is assumed to be almost inviscid in the interior. The heating is assumed …
A coupled discontinuous Galerkin-Finite Volume framework for solving gas dynamics over embedded geometries
2021
Author(s): Gulizzi, Vincenzo; Almgren, Ann S; Bell, John B | Abstract: We present a computational framework for solving the equations of inviscid gas dynamics using structured grids with embedded geometries. The novelty of the proposed approach is the use of high-order discontinuous Galerkin (dG) schemes and a shock-capturing Finite Volume (FV) scheme coupled via an $hp$ adaptive mesh refinement ($hp$-AMR) strategy that offers high-order accurate resolution of the embedded geometries. The $hp$-AMR strategy is based on a multi-level block-structured domain partition in which each level is represented by block-structured Cartesian grids and the embedded geometry is represented implicitly by a…