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In this paper, we derive a thermodynamically consistent non-isothermal diffuse interface model for phase transition and interface evolution involving heat transfer. This model is constructed by integrating concepts from classical…
Surface heat transfer in convective and radiative environments is sometimes measured by recording the surface temperature history in a transient experiment and interpreting this surface temperature with the aid of a suitable model for…
As a first step towards the numerical analysis of the stochastic primitive equations of the atmosphere and oceans, we study their time discretization by an implicit Euler scheme. From deterministic viewpoint the 3D Primitive Equations are…
Three inverse boundary value problems for the heat equations in one space dimension are considered. Those three problems are: extracting an unknown interface in a heat conductive material, an unknown boundary in a layered material or a…
Numerical simulation of steady-state heat conduction is common for thermal engineering. The simulation process usually involves mathematical formulation, numerical discretization and iteration of discretized ordinary or partial differential…
We consider linear iterative schemes for the time-discrete equations stemming from a class of nonlinear, doubly-degenerate parabolic equations. More precisely, the diffusion is nonlinear and may vanish or become multivalued for certain…
The numerical solution of time-dependent radiative transfer problems is challenging, both, due to the high dimension as well as the anisotropic structure of the underlying integro-partial differential equation. In this paper we propose a…
We present a Bayesian model calibration framework for inferring nonlinear constitutive relationships in heat conduction problems, with a focus on temperature-dependent thermal conductivity. The proposed framework integrates gradient-based…
Accurate simulations of ice sheet dynamics, mantle convection, lava flow, and other highly viscous free-surface flows involve solving the coupled Stokes/free-surface equations. In this paper, we theoretically analyze the stability and…
This paper presents a new method to approximate the time-dependent convection-diffusion equations using conforming finite element methods, ensuring that the discrete solution respects the physical bounds imposed by the differential…
In this note we describe a space-time boundary element discretization of the heat equation and an efficient and robust preconditioning strategy which is based on the use of boundary integral operators of opposite orders, but which requires…
A mathematical model of the heat process in one-dimensional domain governed by a cylindrical heat equation with a heat source on the axis $z=0$ and nonlinear thermal coefficients is considered. The developed model is particularly applicable…
Within this paper, we introduce partially and fully decoupled time stepping schemes for linear thermo-poroelasticity. This means that the mechanics, heat, and flow equations can be solved sequentially. We provide sufficient conditions on…
Integro-partial differential equations occur in many contexts in mathematical physics. Typical examples include time-dependent diffusion equations containing a parameter (e.g., the temperature) that depends on integrals of the unknown…
This work presents efficient solution techniques for radiative transfer in the smoothed particle hydrodynamics discretization. Two choices that impact efficiency are how the material and radiation energy are coupled, which determines the…
In ecological studies of pattern formation, models of the competitive-diffusion type are generally singularly perturbed, and the numerical approximation of such models is challenging. In this paper, we present finite element discretization…
It is necessary to use more general models than the classical Fourier heat conduction law to describe small-scale thermal conductivity processes. The effects of heat flow memory and heat capacity memory (internal energy) in solids are…
In the present study, a discrete forcing Immersed Boundary Method (IBM) is proposed for the numerical simulation of high-speed flow problems including heat exchange. The flow field is governed by the compressible Navier-Stokes equations,…
In this paper, we present a Newton-like method based on model reduction techniques, which can be used in implicit numerical methods for approximating the solution to ordinary differential equations. In each iteration, the Newton-like method…
A simplified transient energy-transport system for semiconductors subject to mixed Dirichlet-Neumann boundary conditions is analyzed. The model is formally derived from the non-isothermal hydrodynamic equations in a particular vanishing…