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Chemical reactions occur everywhere in both natural and artificial systems. Some of the reactions occur during the flow of a fluid (such a process is referred to as a reactive flow). Given the hazardous nature of some reactive flows, computer simulations (rather than physical experiments) are necessary for ascertaining or enhancing our understanding of such systems. The process of simulation involves mathematical and numerical modeling of the reactive flows. Mathematical models for reactive flow problems are complicated partial differential equations that often lack exact solutions, thus, numerical solutions are employed. Numerical methods must preserve almost all the relevant properties of the problem for accuracy reasons. Dispersion relations are important properties of wave propagation problems and numerical methods that satisfy them are called dispersion preserving methods. Furthermore, stiff transport models are wave propagation problems that cannot be solved efficiently with explicit methods. However, fully implicit methods are computationally expensive. A combination of implicit and explicit methods called implicit–explicit methods is usually employed to efficiently resolve stiffness. An example of problems of interest in this regard are the advection–diffusion–reaction (ADR) models. In this discussion, spectral analysis is performed on two implicit–explicit methods to ascertain their dispersion preserving abilities in order to determine their suitability for simulating general stiff reactive flow problems. The analysis shows that both implicit–explicit methods are dispersion preserving, however, one particular method is more suitable for general wave propagation problems. [ABSTRACT FROM AUTHOR]

In this paper, we consider simultaneous reconstruction of diffusion coefficient and initial state for a one-dimensional heat equation through boundary control and measurement. The boundary measurement is proposed to make the system approximately observable, and both the coefficient and initial state are shown to be identifiable by this measurement under a boundary switch on/off control. By a Dirichlet series representation for the observation, we can transform the problem into an inverse process of reconstruction of the spectrum and coefficients for the Dirichlet series in terms of observation. This happens to be the reconstruction of spectral data for an exponential sequence with measurement error, and it enables us to develop an algorithm based on the matrix pencil method in signal analysis. A theoretical error analysis for the algorithm concerning the coefficient reconstruction is carried out for the proposed method. The numerical simulations are presented to verify the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, numerical boundary stabilisation of a non-uniform hyperbolic system of balance laws is studied. For the numerical discretisation of the balance laws, a first order explicit upwind scheme is used for the spatial discretisation; and for the temporal discretisation a splitting technique is employed. A discrete L 2 -Lyapunov function is employed to investigate conditions for the stability of the system. After constructing discrete numerical Lyapunov functionals, we prove an asymptotic exponential stability result for a class of non-uniform linear hyperbolic systems of balance laws. Convergence of the solution to its equilibrium is proved. Further application of the approach to practical problems through concrete examples is presented together with suggestions for numerical implementation. The numerical computations also demonstrate the stability of the numerical scheme with parameters chosen to satisfy the stability requirements. [ABSTRACT FROM AUTHOR]

In this paper, simultaneous identification of damping or anti-damping coefficient and initial value for some Riesz spectral systems is considered. An identification algorithm is proposed based on the fact that the output of the systemhappens to be decomposed into a product of an exponential function and a periodic function. The former contains information of the damping coefficient, while the latter does not. The convergence and error analysis are also developed. Three examples, namely an anti-stablewave equation with boundary anti-damping, the Schrödinger equation with internal antidamping and two connected strings with middle joint anti-damping, are investigated and demonstrated by numerical simulations to show the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper deals with an inverse problem of determining the diffusion coefficient, spacewise dependent source term, and the initial value simultaneously for a one-dimensional heat equation based on the boundary control, boundary measurement, and temperature distribution at a given single instant in time. By a Dirichlet series representation for the boundary observation, the identification of the diffusion coefficient and initial value can be transformed into a spectral estimation problem of an exponential series with measurement error, which is solved by the matrix pencil method. For the identification of the source term, a finite difference approximation method in conjunction with the truncated singular value decomposition is adopted, where the regularization parameter is determined by the generalized cross-validation criterion. Numerical simulations are performed to verify the result of the proposed algorithm. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A computational investigation of optimal control problems which are constrained by hyperbolic systems of conservation laws is presented. The general framework is to employ the adjoint-based optimization to minimize the cost functional of matching-type between the optimal and the target solution. Extension of the numerical schemes to second-order accuracy for systems for the forward and backward problem are applied. In addition a comparative study of two relaxation approaches as solvers for hyperbolic systems is undertaken. In particular optimal control of the 1-D Riemann problem of Euler equations of gas dynamics is studied. The initial values are used as control parameters. The numerical flow obtained by optimal initial conditions matches accurately with observations. [ABSTRACT FROM AUTHOR]

In this paper higher order implicit Runge-Kutta schemes are applied to fluid-structure interaction (FSI) simulations. A staggered approach with a structural predictor is applied to an FSI problem. The equations governing the dynamics of the structure are integrated in time by the Explicit Single Diagonal Implicit Runge-Kutta (ESDIRK) schemes and the arbitrary high order finite volume scheme is taken as the fluid solver. The performance of the ESDIRK scheme of order of convergence three to five is tested. Comparative studies with other time integration schemes which have been successfully applied to FSI problems are undertaken. Comparisons to test the performance of the scheme are carried out. The staggered approach is applied to couple the structure and the compressible fluid, therefore the added mass effect is not considered. However the influence of the structural predictors is analyzed through energy conservation. [ABSTRACT FROM AUTHOR]

Suitable numerical discretizations for boundary control problems of systems of nonlinear hyperbolic partial differential equations are presented. Using a discrete Lyapunov function, exponential decay of the discrete solutions of a system of hyperbolic equations for a family of first-order finite volume schemes is proved. The decay rates are explicitly stated. The theoretical results are accompanied by computational results. [ABSTRACT FROM AUTHOR]

The treatment of control problems governed by systems of conservation laws poses serious challenges for analysis and numerical simulations. This is due mainly to shock waves that occur in the solution of nonlinear systems of conservation laws. In this article, the problem of the control of Euler lows in gas dynamics is considered. Numerically, two semi-linear approximations of the Euler equations are compared for the purpose of a gradient-based algorithm for optimization. One is the Lattice-Boltzmann method in one spatial dimension and ive velocities (D1Q5 model) and the other is the relaxation method. An adjoint method is used. Good results are obtained even in the case where the solution contains discontinuities such as shock waves or contact discontinuities. [ABSTRACT FROM AUTHOR]

Abstract: We present a high-order accurate relaxed non-oscillatory scheme for solving magnetohydrodynamic (MHD) equations. The computations reported here demonstrate the remarkable simplicity and versatility of semi-discrete relaxation schemes as solvers for ideal MHD equations. Simulations will be presented for two prototype MHD problems, the one-dimensional Brio–Wu shock tube problems. A qualitative comparison reveals an excellent agreement with previous results based on other approaches. Furthermore, the numerical results demonstrate that such semi-discrete schemes preserve the constraint without necessarily needing the constrained-transport enforcement. [Copyright &y& Elsevier]

Dynamics of multiphase flows through networks are considered. The dynamics of flow through the connected arcs are governed by an isothermal no-slip drift-flux model. Such problems arise in the context of multicomponent flows or in gas transport in pipe networks in which a phase change takes place due to geometrical or physical forces. Coupling conditions for the vertices (joints) in a network have been proposed. We present conditions at and introduce a mathematical representation of the vertex flow for the no-slip drift-flux case of multiphase flows. Mathematical analysis of coupling conditions at the vertices as well as numerical simulations and comparative studies with theoretical predictions are undertaken. [ABSTRACT FROM AUTHOR]

We derive a Godunov-type relaxation scheme for turbulent flows with heat transfer. The building block of this approach is a kinetic Boltzmann-type formulation for a model of turbulent thermal flows based on large-eddy simulation modeling. Discrete-velocity moments are taken in order to derive a relaxation system which is in turn solved by a relaxation scheme. High-order schemes are obtained by discretizing the relaxation system spatially with weighted essentially nonoscillatory reconstruction and temporally using an implicit-explicit discretization. In the limit of small Mach and small Knudsen numbers one obtains a high-order relaxation scheme for large-eddy simulation of turbulent thermal flows. The efficiency, accuracy, and high-resolution properties of the models are demonstrated in a variety of test examples. [ABSTRACT FROM AUTHOR]

In the present paper the low Mach number limit of kinetic equations is used to develop a discretization for the incompressible Navier–Stokes equation. The kinetic equation is discretized with a first- and second-order discretization in space. The discretized equation is then considered in the low Mach number limit. Using this limit a second-order discretization for the convective part in the incompressible Navier–Stokes equation is obtained. Numerical experiments are shown comparing different approaches. [Copyright &y& Elsevier]

In the present paper the low Mach number limit of kinetic equations is used to develop a discretization for the incompressible Euler equation. The kinetic equation is discretized with a first and second order discretization in space. The discretized equation is then considered in the limit of low Mach and Knudsen number which gives rise to an interesting limiter for the convective part in the incompressible Euler equation. Numerical experiments are shown comparing different approaches. [ABSTRACT FROM AUTHOR]