hyperbolic type transport equations abstract in recent years hyperbolic type transport equations have acquired a great deal of importance in problems ranging from theoretical physics to biology in spite of their greater mathematical difficulty as compared with their parabolic type analogs arising from the framework of linear irreversible thermodynamics they have in many ways superseded the latter ones although the use of this type of equations is well known since the last century through the telegraphist equation of electromagnetic theory their use in studying several problems in transport theory is hardly fifty years old in fact the first appearance of a hyperbolic type transport equation for the problem of heat conduction dates back to cattaneos work in 1948 three years later in 1951 s goldstein showed how in the theory of stochastic processes this type of an equation is obtained in the continuous limit of a one dimensional persistent random walk problem after that other phenomenological derivations have been offered for such equations the main purpose of this paper is to critically discuss a derivation of a hyperbolic type fokker planck equation recently presented using the same ideas as m s green did in 1952 to provide the stochastic foundations of irreversible statistical mechanics arguments are given to show that such an equation as well as transport equations derived from it by taking appropriate averages are at most approximate and that a much more detailed analysis is required before asserting their validity

fractional diffusion waiting time distributions and cattaneo type equations we discuss a generalized diffusion equation resulting from an additive two state process in combination with an asymptotically fractal asymptotic power law waiting time distribution the obtained equation is an extension to previously discussed fractional diffusion equations our description leads to a mean squared displacement which describes enhanced subballistic transport for long times the short time behavior however is of a ballistic nature this separation into two domains results from the introduction of a time scale through the asymptotically fractal waiting time distribution this is also mirrored by the observation that for small times our generalized diffusion equation reduces to the standard cattaneo equation the asymptotic probability density is of compressed gaussian type and thus differs from the l evy tail generally found for these kinds of processes

a matrix stability analysis of the carbuncle phenomenon the carbuncle phenomenon is a shock instability mechanism which ruins all efforts to compute grid aligned shock waves using low dissipative upwind schemes the present study develops a stability analysis for two dimensional steady shocks on structured meshes based on the matrix method the numerical resolution of the corresponding eigenvalue problem confirms the typical odd even form of the unstable mode and displays a mach number threshold effect currently observed in computations furthermore the present method indicates that the instability of steady shocks is not only governed by the upstream mach number but also by the numerical shock structure finally the source of the instability is localized in the upstream region providing some clues to better understand and control the onset of the carbuncle

use of a rotated riemann solver for the two dimensional euler equations a scheme for the two dimensional euler equations that uses flow parameters to determine the direction for upwind differencing is described this approach respects the multi dimensional nature of the equations and reduces the grid dependence of conventional schemes several angles are tested as the dominant upwinding direction including the local flow and velocity magnitude gradient angles roe s approximate riemann solver is used to calculate fluxes in the upwind direction as well as for the flux components normal to the upwinding direction the approach is first tested for two dimensional scalar convection where the scheme is shown to have accuracy comparable to a high order muscl scheme solutions of the euler equations are calculated for a variety of test cases substantial improvement in the resolution of shock and shear waves is realized the approach is promising in that it uses flow solution features rather than grid features to determine the orientation for the solution method

anomalous transport in external fields continuous time random walks and fractional diffusion equations extended the continuous time random walk ctrw in a homogeneous velocity field and in arbitrary force fields is studied within the extended ctrw scheme anomalous transport properties due to long tailed waiting time or jump length distributions are consistently introduced the connections with generalised diffusion equations in a potential field are discussed these equations being of fractional order in particular the problems of a constant and a hookean linear force i e of a linear and a parabolic potential are worked out

a high order extension for the cattaneo s diffusion equation abstract in this paper a high order generalization of the diffusion cattaneo s equation is considered a class of admissible linear relaxation dynamics is characterized by computing the impedance of a simple diffusion process some examples are used to illustrate the results

equivalent acoustic impedance model part 2 analytical approximation abstract in the context of the prediction of noise levels in vibroacoustic systems numerical models or analytical models can be developed generally numerical models are adapted to the low and medium frequency ranges and analytical models to the medium and high frequency ranges for analytical models a classical approximation consists of modelling the multilayer system by an equivalent acoustic impedance this paper deals with a multilayer system consisting of a porous medium inserted between two thin plates part 1 of this paper is devoted to the experiments performed and to the development of a probabilistic algebraic model for the equivalent acoustic impedance in the present part 2 an analytical method is constructed for this multilayer system this method consists of introducing the unbounded medium in the plane directions x1 and x2 while the medium is bounded in the x3 direction a two dimensional space fourier transform introducing the wave vector co ordinates k1 and k2 is used for a given frequency and for k1 and k2 fixed the boundary value problem in x3 consists of 12 differential equations in x3 whose coefficients depend on k1 and k2 with boundary conditions this system of equations is solved by using adapted algebraic calculations by inverse fourier transform with respect to k1 and k2 the equivalent acoustic impedance is deduced the method which is proposed is not usual finally a comparison of this analytical approach is compared with the experimental results

scale invariant motion in intermittent chaotic systems we investigate the dynamics generated from iterated maps and analyze the motion in terms of the probabilistic continuous time random walk ctrw approach two different ctrw models are considered i particles jump between sites turning points or ii particles move at a constant velocity between sites and choose a new direction at random for both models we study the mean squared displacement mathit r 2 t and the propagator p r t the probability to be at location r at time t having started at the origin at t 0 iterated maps are used to generate both dispersive and enhanced diffusion and the results are analyzed using the ctrw framework and scaling arguments for the case of dispersive motion we discuss the problem of the stationary state and point out its relevance

general procedure for riemann solver to eliminate carbuncle and shock instability a novel procedure for the riemann solver flux calculation is proposed in this paper with this simple normal velocity reconstruction procedure all of the commonly used flux solvers such as goduno

interface conditions for biot s equations of poroelasticity interface conditions at a boundary between two porous media are derived directly from biot s equations of poroelasticity by replacing the discontinuity surface with a thin transition layer in which the properties of the medium change rapidly yet continuously and then taking the limit as the thickness of the transition layer approaches zero the interface conditions obtained in this way the well known open pore conditions are shown to be the only ones that are fully consistent with the validity of biot s equations throughout the poroelastic continuum including surfaces across which the medium properties are discontinuous but partially blocked or completely impermeable interfaces exist these may be looked upon as the case of a thin layer with its permeability taken to be proportional to the layer thickness again in the limit as layer thickness approaches zero this approach can serve as a simple recipe for modeling such an interface in any heterogeneous numerical scheme for poroelastic media

fractional model equation for anomalous diffusion abstract in recent years the phenomenon of anomalous diffusion has attracted more and more attention one of the main impulses was initiated by de gennes idea of the ant in the labyrinth several authors presented asymptotic probability density functions for the location of a random walker on a fractal object as this density function and the time dependence of its second moment are now well established a modified diffusion equation providing the correct result is formulated the parameters of this fractional partial differential equation are uniquely determined by the fractal hausdorff dimension of the underlying object and the anomalous diffusion exponent the presented equation reduces exactly to the ordinary isotropic diffusion equation by appropriate choice of the parameters a closed form solution is given in terms of fox s h function in the asymptotic case a halved diffusion equation can be established furthermore the differences to equations considered previously are discussed

stochastic foundations of fractional dynamics it is shown that fractional diffusion equations arise very naturally as the limiting dynamic equations of all continuous time random walks with decoupled temporal and spatial memories and with either temporal or spatial scale invariance fractal walks thus enlarging their stochastic foundations hitherto restricted to a particular case of fractal walk r hilfer and l anton phys rev e 51 r848 1995

an efficient finite element scheme for solving the three dimensional poroelasticity problem in acoustics in this paper the finite element method fem is used to solve the three dimensional poroelasticity problem in acoustics based on the isotropic biot allard theory a displacement finite element model is derived using the lagrangian approach together with an analogy with solid elements from this model it is seen that the damping and stiffness matrices of the poroelastic media are complex and frequency dependent this leads to cumbersome calculations for large finite element models and spectral analyses to overcome this difficulty an efficient algorithm is proposed it is based on low frequency approximations of the frequency dependent dissipation mechanisms in poroelastic media this efficient algorithm allows the poroelastic materials to be modeled with classical fem codes also the acoustic poroelastic and the poroelastic poroelastic coupling conditions are presented the proposed model is compared to existing literature for both two dimensional and three dimensional problems excellent compari

two dimensional telegraphic processes and their fractional generalizations we study the planar motion of telegraphic processes we derive the two dimensional telegrapher s equation for isotropic and uniform motions starting from a random walk model which is the two dimensional version of the multistate random walk with a continuum number of states representing the spatial directions we generalize the isotropic model and the telegrapher s equation to include planar fractional motions earlier we worked with the one dimensional version masoliver phys rev e 93 052107 2016 prehbm2470 004510 1103 physreve 93 052107 and derived the three dimensional version masoliver phys rev e 96 022101 2017 prehbm2470 004510 1103 physreve 96 022101 an important lesson is that we cannot obtain the two dimensional version from the three dimensional or the one dimensional one from the two dimensional result each dimension must be approached starting from an appropriate random walk model for that dimension

a second order projection method for the incompressible navier stokes equations in this paper we describe a second order projection method for the time dependent incom pressible navier stokes equations as in the original projection method developed by chorin we first solve diffusion convection equations to predict intermediate velocities which are then projected onto the space of divergence free vector fields by introducing more coupling between the diffusion onvection step and the projection step we obtain a temporal discretiza tion that is second order accurate our treatment of the diffusion convection step uses a specialized higher order godunov method for differencing the nonlinear convective terms that provides a robust treatment of these terms at high reynolds number the godunov procedure is second order accurate for smooth flow and remains stable for discontinuous initial data even in the zero viscosity limit we approximate the projection directly using a galerkin procedure that uses a local basis for discretely divergence free vector fields numerical results are presented validating the convergence properties of the method we also apply the method to doubly periodic shear layers to assess the performance of the method on more difficult

aon waf type schemes for multidimensional hyperbolic conservation laws we explore how the weighted average flux approach can be used to generate first and second order accurate finite volume schemes for the linear advection equatons in one two and three space dimensions the derived schemes have multidimensional upwinding aspects and good stability properties from the two dimensional methods we construct a scheme for nonlinear systems of hyperbolic conservation laws that is second order accurate in smooth flow spurious oscillations are controlled by making use of one dimensional tvd limiter functions numerical results are presented for the shallow water equations in two space dimensions the equivalent schemes are derived for nonlinear systems in three space dimensions

evolution of the initial box signal for time fractional diffusion wave equation in a case of different spatial dimensions abstract in the case of time fractional diffusion wave equation considered in the spatial domain x evolution of initial box signal was investigated by mainardi f mainardi fractional relaxation oscillation and fractional diffusion wave phenomena chaos solitons fractals 7 1996 1461 1477 in the present paper we supplement mainardi s results with additional numerical calculations illustrating the behavior of the solution and solve the corresponding problems for axisymmetric and central symmetric cases the obtained results show an unusual behavior of solutions

the generalized cattaneo equation for the description of anomalous transport processes the cattaneo equation which describes a diffusion process with a finite velocity of propagation is generalized to describe anomalous transport three possible generalizations are proposed each one supported by a different scheme continuous time random walks non local transport theory and delayed flux force relation the properties of these generalizations are studied in both the long time and the short time regimes in the long time limit we recover the mean square displacement which is characteristic for these anomalous processes as expected the short time behaviour is modified in comparison to generalized diffusion equations

on the time fractional cattaneo equation of distributed order abstract the present work revisits the time fractional cattaneo equation tfce by considering a generic class of time fractional derivatives of distributed order 0 1 at first we shed light on two main forms of tfce one natural generalization uses the caputo fractional derivative and the other compte metzler generalization is defined in the riemann liouville sense and the equivalence condition between their solutions is provided some special cases of these two forms are addressed hence different versions of distributed order tfce are proposed the fundamental solution of the two general forms of distributed order tfce are derived using integral transform technique the non negativity of solutions of tfce and its distributed order versions is examined using the special type functions technique gorenflo luchko and stojanovic 2013 two classes of order distribution are considered discrete order and continuous order distributions and some random choices of non negative order densities affirm graphically the non negativity of the general forms of distributed order tfce the double order as an example on the discrete order and exponentially exp and sinusoidally sin distributed order as an example on the continuous order are chosen finally connections between some models of distributed order tfce and continuous time random walk theory are established and the corresponding mean squared displacements are discussed

enhanced weak integral formulation for the mixed u_ p_ poroelastic equations recently atalla et al j acoust soc am 104 1444 1452 1998 and debergue et al j acoust soc am 106 2383 2390 1999 presented a weak integral formulation and the general boundary conditions for a mixed pressure displacement version of the biot s poroelasticity equations finite element discretization was applied to the formulation to solve 3d vibro acoustic problems involving elastic acoustic and poroelastic domains in this letter an enhancement of the weak integral formulation is proposed to facilitate its finite element implementation it is shown that this formulation simplifies the assembly process of the poroelastic medium the imposition of its boundary conditions and its coupling with elastic and acoustic media

upwind schemes and boundary conditions with applications to euler equations in general geometries abstract a unified treatment of several upwind shock capturing algorithms is presented each algorithm has a riemann initial value problem as its basis the treatment of boundaries involves solving the associated riemann initial boundary value problem the first author s algorithm applied to multidimensional euler equations in general geometries is then presented its worth is verified by various calculations which include mach 8 supersonic flow past a circular cylinder

stochastic foundation of normal and anomalous cattaneo type transport abstract we investigate the connection of the cattaneo equation and the stochastic continuous time random walk ctrw theory we show that the velocity model in a ctrw scheme is suited to derive the standard cattaneo equation and allows in principle for a generalisation to anomalous transport as a result for a broad waiting time distribution with diverging mean we find a strong memory to the initial condition of the system the ballistic behaviour subsists also for long times only if a characteristic waiting time exists a non ballistic enhanced motion is found in the limit of long times no transition to subdiffusion can be found

fractional master equations and fractal time random walks fractional master equations containing fractional time derivatives of order 0 ensuremath le 1 are introduced on the basis of a recent classification of time generators in ergodic theory it is shown that fractional master equations are contained as a special case within the traditional theory of continuous time random walks the corresponding waiting time density ensuremath psi t is obtained exactly as ensuremath psi t mathit t mathrm ensuremath omega mathrm ensuremath 1 c mathit e mathrm ensuremath omega mathrm ensuremath omega mathit t mathrm ensuremath omega c where mathit e mathrm ensuremath omega mathrm ensuremath omega x is the generalized mittag leffler function this waiting time distribution is singular both in the long time as well as in the short time limit

robust hllc riemann solver with weighted average flux scheme for strong shock many researchers have reported failures of the approximate riemann solvers in the presence of strong shock this is believed to be due to perturbation transfer in the transverse direction of shock waves we propose a simple and clear method to prevent such problems for the harten lax van leer contact hllc scheme by defining a sensing function in the transverse direction of strong shock the hllc flux is switched to the harten lax van leer hll flux in that direction locally and the magnitude of the additional dissipation is automatically determined using the hll scheme we combine the hllc and hll schemes in a single framework using a switching function high order accuracy is achieved using a weighted average flux waf scheme and a method for v shear treatment is presented the modified hllc scheme is named hllc hll it is tested against a steady normal shock instability problem and quirk s test problems and spurious solutions in the strong shock regions are successfully controlled

two dimensional axisymmetric stresses exerted by instantaneous pulses and sources of diffusion in an infinite space in a case of time fractional diffusion equation the theory of diffusive stresses based on the time fractional diffusion equation is formulated the source problem is discussed as well as the cauchy problem the stresses are found in axially symmetric cases for plane deformation the numerical results for the concentration and stress distributions are presented graphically for various values of order of fractional derivative

a new flux splitting scheme a new flux splitting scheme is proposed the scheme is remarkably simple and yet its accuracy rivals and in some cases surpasses that of roe s solver in the euler and navier stokes solutions carried out in this study the scheme is robust and converges as fast as the roe splitting we propose an appropriately defined cell face advection mach number using values from the two straddling cells via associated characteristic speeds this interface mach number is then used to determine the upwind extrapolation for the convective quantities accordingly the name of the scheme is coined as the advection upstream splitting method ausm we also introduce a new pressure splitting which is shown to behave successfully yielding much smoother results than other existing pressure splittings of particular interest is the supersonic blunt body problem in which the roe scheme gives anomalous solutions the ausm produces correct solutions without difficulty for a wide range of flow conditions as well as grids

nonlinear heat conduction equations with memory physical meaning and analytical results we study nonlinear heat conduction equations with memory effects within the framework of the fractional calculus approach to the generalized maxwell cattaneo law our main aim is to derive the governing equations of heat propagation considering both the empirical temperature dependence of the thermal conductivity coefficient which introduces nonlinearity and memory effects according to the general theory of gurtin and pipkin of finite velocity thermal propagation with memory in this framework we consider in detail two different approaches to the generalized maxwell cattaneo law based on the application of long tail mittag leffler memory function and power law relaxation functions leading to nonlinear time fractional telegraph and wave type equations we also discuss some explicit analytical results to the model equations based on the generalized separating variable method and discuss their meaning in relation to some well known results of the ordinary case

the restaurant at the end of the random walk recent developments in the description of anomalous transport by fractional dynamics fractional dynamics has experienced a firm upswing during the past few years having been forged into a mature framework in the theory of stochastic processes a large number of research papers developing fractional dynamics further or applying it to various systems have appeared since our first review article on the fractional fokker planck equation metzler r and klafter j 2000a phys rep 339 1 77 it therefore appears timely to put these new works in a cohesive perspective in this review we cover both the theoretical modelling of sub and superdiffusive processes placing emphasis on superdiffusion and the discussion of applications such as the correct formulation of boundary value problems to obtain the first passage time density function we also discuss extensively the occurrence of anomalous dynamics in various fields ranging from nanoscale over biological to geophysical and environmental systems

equivalent acoustic impedance model part 1 experiments and semi physical model the context of this research is devoted to the construction of an equivalent acoustic impedance model for a soundproofing scheme consisting of a three dimensional porous medium inserted between two thin plates part 1 of this paper presents the experiments performed and a probabilistic algebraic model of the wall acoustic impedance constructed using the experimental data basis for the medium and high frequency ranges the probabilistic algebraic model is constructed by using the general mathematical properties of wall acoustic impedance operators symmetry odd and even functions with respect to the frequency decreasing functions when frequency goes to infinity behaviour when frequency goes to zero and so on the parameters introduced in this probabilistic algebraic model are fitted with the experimental data basis finally this probabilistic algebraic model summarizes all the experimental data bases and consequently can be reused for other researches