Application of meshfree methods for solving the inverse one-dimensional Stefan problem

Determination of one or two unknown thermal coefficients of a semi-infinite material through a two-phase stefan problem

Determination of a spacewise dependent heat source

In this paper, we consider inverse problems of finding the time-dependent source function for the population model with population density nonlocal boundary conditions and an integral over-determination measurement. These problems arise in mathematical biology and have never been investigated in the literature in the forms proposed, although related studies do exist. The unique solvability of the inverse problems are rigorously proved using generalized Fourier series and the theory of Volterra integral equations. Continuous dependence on smooth input data also holds but, as in reality noisy errors are random and non-smooth, the inverse problems are still practically ill-posed. The degree of ill-posedness is characterised by the numerical differentiation of a noisy function. In the numerical process, the boundary element method together with either a smoothing spline regularization or the first-order Tikhonov regularization are employed with various choices of regularization parameter. One is based on the discrepancy principle and another one is the generalized cross-validation criterion. Numerical results for some benchmark test examples are presented and discussed in order to illustrate the accuracy and stability of the numerical inversion.

Stefan problem is a problem involving phase transition from solid to liquid or vice versa where boundary between solid and liquid regions moves as function of time. This paper presents numerical solution of one-dimensional two-phase Stefan problem by using finite element method. The governing equations involved in Stefan problem consist of heat conduction equation for solid and liquid regions, and also transition equation in interface position (moving boundary). The equations are difficult to solve by ordinary numerical method because of the presence of moving boundary. As consequence, the equations is reformulated into the form of internal energy (enthalpy). By the enthalpy formulation, solution of the heat conduction equations is no longer concerning the phase state of material. The advantage of the enthalpy formulation is that, finite element method can be easily implemented to solve Stefan problem. Numerical simulation of interface position, temperature profile, and temperature history has good agreement with the exact solution. The approximation of interface position using finite element method was found that it is more accurate than the approximation by using Godunov method. The simulation results also reveal that the finite element method for solving Stefan problem have smaller mean absolute error than the Godunov method.

Asymptotic analysis of a two-phase Stefan problem in annulus: Application to outward solidification in phase change materials

Space-dependent heat source determination problem with nonlocal periodic boundary conditions

The classical Stefan problem proffers a suitable model for determining the temperature regimes as well as conjugate interfacial positions for multiphase problems. Obtaining the solutions to these problems exactly, especially in systems with cylindrical or spherical symmetry, is often an arduous task. This is largely due to inherent nonlinearities in the mathematical statements of Stefan problems. In this paper, a tractable and effective approach is proposed. Subsequent to a recast as a system of differential-difference equations, and a methodical reduction to constant coefficient difference equations, exact similarity solutions are derived for a class of heterogeneous two-phase Stefan problems with cylindrical or spherical symmetry in one spatial dimension, under either Gaussian or hypergeometric perturbations.

A diffuse interface–lattice Boltzmann model for conjugate heat transfer with imperfect interface

Inverse two-phase nonlinear Stefan and Cauchy-Stefan problems: A phase-wise approach

Laplacian decomposition and the boundary element method for solving Stokes problems

Transportation planning and path planning are hot research topics which can be evidenced by their frequent and repeated presence in the benchmark test in International Planning Competition. However, most of the benchmark test examples only consider the static planning problems, whose state transitions are only caused by the actions of the planners. In this paper, we will discuss the dynamic version and introduce the formalization of the Period/Dynamic planning problem. Then, we will prove that the computational complexity is EXPSPACE-Complete.

Advanced Dynamics has developed an Integrated Variable-Fidelity Tool Set – ASTE-P for Modeling and Simulation of Aero-Servo-Thermo-Elasticity and Propulsion (ASTE-P) of Aerospace Vehicles Ranging from Subsonic to Hypersonic Flights. The ASTE-P software tool set is developed in the state-of-the-art and commercial standard and enables accurate integration and tight/loose coupling of the fluid, structural and control field simulation with variable fidelity options available. The ASTE-P software tool can be applicable to modeling and simulation of aerodynamics, structural dynamics, flight control and propulsion dynamics as well as more important interactions of these dynamics. All flight regimes from subsonic to hypersonic are covered. The interface of structural/control surface motion and vibration modes with fluid flows is modeled using either unified particle-based methods (MPM/PPM) or FVM/FEM based tight/loose coupled fluid/structure solving algorithms. The Euler and RANS based solvers enable the accurate prediction of nonlinear coupled fluidstructure problems in aeroelasticity and the embedded fluid and structural dynamics solvers make the software self-contained and not require the integration of two separate third-party fluid and structure solvers for aeroelastic modeling and simulation. Three levels of simulation environments are included in ASTE-P tool set: (1) the bottom level of high-fidelity and full-order simulation environment, (2) middle level of fast analysis and evaluation environment which is based upon reduced order models (ROM) and provides fast turn-around time, and (3) top level of rapid design and optimization environment. This paper provides the comprehensive validation and verification (V&V) of ASTE-P toolset recently done at Advanced Dynamics which resulted in over 600 pages report for over 40 benchmark test examples that were selected from industry and academic research and design . The validation cases presented in this paper indicate that the capability of ASTE-P is compatible or even more powerful than the similar software that is currently available.

An integral equation method for spherical Stefan problems

We provide existence of a unique smooth solution for a class of one-and two-phase Stefan problems with Gibbs-Thomson correction in arbitrary space dimensions.In addition, it is shown that the moving interface depends analytically on the temporal and spatial variables.Of crucial importance for the analysis is the property of maximal L pregularity for the linearized problem, which is fully developed in this paper as well.

Solution of two-phase Stefan's problem for cylindrical domain