Cristian A. Coclici

The coupling of hyperbolic and elliptic boundary value problems with variable coefficients

We consider a one-dimensional coupled problem for elliptic second-order ODEs with natural transmission conditions. In one subinterval, the coefficient e > 0 of the second derivative tends to zero. Then the equation becomes there hyperbolic and the natural transmission conditions are not fulfilled anymore. The solution of the degenerate coupled problem with a flux transmission condition is corrected by an internal boundary layer term taking into account the viscosity e. By using singular perturbation techniques, we show that the remainders in our first-order asymptotic expansion converge to zero uniformly. Our analysis provides an a posteriori correction procedure for the numerical treatment of exterior viscous compressible flow problems with coupled Navier-Stokes/Euler models.

ANALYSIS OF A HETEROGENEOUS DOMAIN DECOMPOSITION FOR COMPRESSIBLE VISCOUS FLOW

We analyze a nonoverlapping domain decomposition method for the treatment of two-dimensional compressible viscous flows around airfoils. Since at some distance to the given profile the inertial forces are strongly dominant, there the viscosity effects are neglected and the flow is assumed to be inviscid. Accordingly, we consider a decomposition of the original flow field into a bounded computational domain (near field) and a complementary outer region (far field). The compressible Navier–Stokes equations are used close to the profile and are coupled with the linearized Euler equations in the far field by appropriate transmission conditions, according to the physical properties and the mathematical type of the corresponding partial differential equations. We present some results of flow around the NACA0012 airfoil and develop an a posteriori analysis of the approximate solution, showing that conservation of mass, momentum and energy are asymptotically attained with the linear model in the far field.

Heterogeneous Domain Decomposition Methods for Compressible Magneto-plasma Flows

We present nonoverlapping domain decomposition methods for the numerical treatment of compressible viscous plasma flows inside a self—field magnetoplasmadynamic (MPD) accelerator. The magneto—plasma flow is modelled by a system of conservation laws extended by partial differential equations describing the electromagnetic field. Since the numerical solution of the governing equations is extremely expensive, the flow—field domain is decomposed into two or three model zones, characterized by different physical properties of the flow. The compressible Navier—Stokes equations (extended under the influence of an arc discharge) in the near field of the accelerator are coupled with simplified models of extended conservation laws in the far field via appropriate transmission conditions at the artificial coupling boundaries. Results of our numerical computations are presented.

Magnetoplasmadynamic rocket thruster simulation

Magnetoplasmadynamic (MPD) rocket thrusters are investigated numerically and experimentally at the Institut fur Raumfahrtsysteme (IRS). The self-magnetic plasma flow in thermal and reaction non-equilibrium is modeled with thirteen conservation equations. A new finite volume solver has been developed to compute the steady-state solution. The upwinding scheme for the species and the time-stepping procedure will be described in detail, and numerical results for the hot anode thruster will be presented.

On the Treatment of the Kutta-Joukowski Condition in Transonic Flow Computations

A finite element-boundary element compling procedure is applied to the computation of a transonic, compressible full potential flow past an airfoil. We require the Kutta-Joukowski condition as continuity of the pressure field at the trailing edge, Under the assumption of subsonic flow at the trailing edge and using classical regularity results for the solutions of elliptic first order systems, we prove the Holder continuity of the velocity in a vicinity of the trailing edge and get a local representation formula for the velocity. The Kutta-Joukowski condition enforces that the so-called stress intensity factor in this representation vanishes. The numerical FEM-BEM coupling procedure is executed in spaces of finite element functions charaeterized by the linear side condition of vanishing approximate stress intensity factors. The lincar side condition is formulated in terms of the Maz ya functional for the stress intensity factor. Detailed numerical implementation and numerical results are presented.

Artificial outlet boundary conditions for steady flows with rotational symmetry

We present a construction of far-field boundary conditions on the outflow cross-section for axisymmetric two-dimensional compressible flows in a pipe. An unbounded downstream domain is considered, where the original subsonic flow is modelled via steady compressible Euler equations linearized about its mean value. The resulting system for the perturbations leads in particular to an exterior elliptic problem for the pressure. Its solution, calculated by means of Fourier analysis, provides the Dirichlet-to-Neumann map at the open boundary defining artificial boundary conditions in the form of the Steklov-Poincare operator. We present a method for the approximation of this operator and exemplify our procedure for the case of a compressible plasma flow inside a self-field magnetoplasmadynamic accelerator.

Asymptotic analysis of coupled problems for compressible flows

We consider a two-dimensional coupled transmission problem with the conservation laws for compressible viscous flows, where in a subdomain of the flow-field domain the terms modelling the viscosity and heat conductivity effects are strongly dominated by the convective part. In order to approximate the physical solution, we construct a reduced problem including the Navier-Stokes/Euler coupling of equations. An asymptotic analysis based on singular perturbation theory includes vector-valued boundary layer functions which are used in order to establish transmission conditions at the artificial interface and to improve the solution of the reduced coupled problem. We present numerical results confirming our asymptotic analysis, and an application associated with magneto-plasma-dynamic (MPD) flows.