Related papers: Shock equations and jump conditions for the 2D Adj…
In this paper, we proved the well-posedness theory of compressible subsonic jet flows for two-dimensional steady Euler system with {\it general} incoming horizontal velocity as long as the flux is larger than a critical value. One of the…
We formulate the quasi-static elastic contact problem with Coulomb friction in a very general setting, with possible jumps in time for both the load and the solution. Exploiting ideas originating in our recent paper [4], we exhibit an…
The fully discrete adjoint equations and the corresponding adjoint method are derived for a globally high- order accurate discretization of conservation laws on parametrized, deforming domains. The conservation law on the deforming domain…
We consider the conductivity problem in the presence of adjacent circular inclusions having arbitrary constant conductivity. When two inclusions get closer and their conductivities degenerate to zero or infinity, the gradient of the…
In this paper we investigate the stress concentration problem that occurs when two convex rigid particles are closely immersed in a fluid flow. The governing equations for the fluid flow are the stationary incompressible Navier-Stokes…
In the paper, we are concerned with degenerate stochastic differential equations with jumps. Firstly, we establish two support theorems for the solutions of the degenerate stochastic equations, under different (sufficient) conditions.…
The boundary conditions prescribing the constant traction or the so-called do-nothing conditions are frequently taken on artificial boundaries in the numerical simulations of steady flow of incompressible fluids, despite the fact that they…
We present a rigorous approach and related techniques to construct global solutions of the 2-D Riemann problem with four-shock interactions for the Euler equations for potential flow. With the introduction of three critical angles: the…
A new procedure to capture the shocks has been proposed and is demonstrated for the solutions of two-dimensional Euler equations using discontinuous Galerkin method and overset grids. A discontinuous Galerkin solver using a coarse grid…
We study two classes of linear difference differential equations analogous to Euler-Cauchy ordinary differential equations, but in which multiple arguments are shifted forward or backward by fixed amounts. Special cases of these equations…
On the example of two-phase continua experiencing stress induced solid-fluid phase transitions we explore the use of the Euler structure in the formulation of the governing equations. The Euler structure guarantees that solutions of the…
The aim of this paper is to investigate the response of this system/scheme in terms of stability in presence of explicitly treated residual terms, as it inevitably occurs in the reality of NWP. This sudy is restricted to the impact of…
Subsurface flows are commonly modeled by advection-diffusion equations. Insufficient measurements or uncertain material procurement may be accounted for by random coefficients. To represent, for example, transitions in heterogeneous media,…
On the basis of the viscous Saint-Venant equations, hydraulic jumps in laminar open channel flow are obtained as continuous shock structures. Thanks to the inclusion of viscosity, the jumps are not abrupt, rendering the classic patchwork…
The advection equation is the basis for mathematical models of continuum mechanics. In the approximate solution of nonstationary problems it is necessary to inherit main properties of the conservatism and monotonicity of the solution. In…
In this paper, we are concerned with the existence of transonic shock solutions for two-dimensional (2-d) steady Euler flows of polytropic gases with the vertical gravity in a horizontal nozzle under a pressure condition imposed at the exit…
Consider a one-dimensional stochastic differential equation with jumps $$\mathrm d X(t) = a(X(t))\mathrm d t + \sum_{k = 1}^m b_k(X(t-))\mathrm d Z_k(t),$$ where $Z_k, \ k \in \{1, 2, ..., m\}$ are independent centered L\'evy processes with…
Strong discontinuities in solutions of the gas dynamic equations under isentropic conditions, i.e., with continuity of entropy at the discontinuity, are examined. Solutions for a standard shock wave with continuity of energy at the…
Hodograph equations for the n-dimensional Euler equations with the constant pressure and external force linear in velocity are presented. They provide us with solutions of the Euler in implicit form and information on existence or absence…
We investigate the dependence on parameters for second order difference equations with two point boundary value conditions by using a variational method in case when the corresponding Euler action functional is coercive. Some applications…