Amacroscopic two-fluid model of compressible particle-laden gas flows is considered. The governing equations are discretized by a high-resolution finite element method based on algebraic flux correction. A multidimensional limiter of TVD type is employed to constrain the local characteristic variables for the continuous gas phase and conservative fluxes for a suspension of solid particles. Spec...

Abstract. A general procedure to construct a class of simple and efficient high resolution Total Variation Diminishing (TVD) schemes for non-linear hyperbolic conservation laws by introducing anti-diffusive terms with the flux limiters is presented. In the present work the numerical flux function for space discretization is constructed as a combination of numerical flux function of any entropy ...

A code using the MacCormack scheme modified t o be TVD has been written t o analyze the flow in a magnetohydrodynamic conductivity channel driven by a reflected shock tube with a heated driver. Items considered include the thermodynamic and electrical properties of the potassium-seeded plasma, both with and without a current applied along the flow, and the steady-state test t ime in the channel...

The quantification of uncertainties is critical when systems are nonlinear and have uncertain terms in their governing equations or are constrained by limited knowledge of initial and boundary conditions. Such situations are common in multiscale, intermittent and nonhomogeneous fluid and ocean flows. The dynamically orthogonal (DO) field equations provide an adaptive methodology to predict the ...

We present some difference approximation schemes which converge to the entropy solution of a scalar conservation law having a convex flux. The numerical methods described here take their origin from approximation schemes for Hamilton-Jacobi-Bellman equations related to optimal control problems and exhibit several interesting features: the convergence result still holds for quite arbitrary time ...

The algebraic flux correction (AFC) paradigm is extended to finite element discretizations with a consistent mass matrix. A nonoscillatory low-order scheme is constructed by resorting to mass lumping and conservative elimination of negative off-diagonal coefficients from the discrete transport operator. In order to recover the high accuracy of the original Galerkin scheme, a limited amount of c...

The receptivity of a Mach 5.92 flat plate boundary layer to periodic two-dimensional wall perturbations is studied by numerical simulations and linear stability theory LST . Free stream flow conditions are the same as the leading edge receptivity experiment of Maslov et al., J. Fluid Mech. 426, 73 2001 . Steady base flow is simulated by solving compressible Navier–Stokes equations with a combin...

In this paper we present an error estimate for the explicit Runge-Kutta discontinuous Galerkin method to solve linear hyperbolic equation in one dimension with discontinuous but piecewise smooth initial data. The discontinuous finite element space is made up of piecewise polynomials of arbitrary degree, and time is advanced by the third order explicit total variation diminishing Runge-Kutta met...

We present a simplified h-box method for integrating time-dependent conservation laws on embedded boundary grids using an explicit finite volume scheme. By using a method of lines approach with a strong stability preserving Runge–Kutta method in time, the complexity of our previously introduced h-box method is greatly reduced. A stable, accurate, and conservative approximation is obtained by co...

We present a new multi–fluid, grid MHD code PIERNIK, which is based on the Relaxing TVD scheme. The original scheme has been extended by an addition of dynamically independent, but interacting fluids: dust and a diffusive cosmic ray gas, described within the fluid approximation, with an option to add other fluids in an easy way. The code has been equipped with shearing–box boundary conditions, ...