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We introduce novel finite element schemes for curve diffusion and elastic flow in arbitrary codimension. The schemes are based on a variational form of a system that includes a specifically chosen tangential motion. We derive optimal $L^2$-…
This work presents an alternative view on the numerical simulation of diffusion processes applied to the heat and moisture transfer through porous building materials. Traditionally, by using the finite-difference approach, the…
Thermal diffusivity measurements of samples transmitting thermal radiation require adjustments to the data treatment procedures in laser flash analysis. Conventionally, an unconstrained diathermic model is used. Current results show that…
Transition state calculation is a critical technique to understand and predict versatile dynamical phenomena in solids. However, the transition state results obtained at zero Kelvin are often utilized for prediction or interpretation of…
Transient dynamics of heat conduction in isotropic fractal metamaterials is investigated. By using the Laplacian operator in non-integer dimension, we analytically and numerically study the effect of fractal dimensionality on the evolution…
A theoretical model is developed for the forced convection film boiling phenomenon over a heated sphere moving vertically downwards in the water. Unprecedented to the previous analytical studies, this model accounts for the buoyancy effects…
In this short note we investigate the numerical performance of the method of artificial diffusion for second-order fully nonlinear Hamilton-Jacobi-Bellman equations. The method was proposed in (M. Jensen and I. Smears, arxiv:1111.5423);…
We study the weak finite element method solving convection-diffusion equations. A weak finite element scheme is presented based on a spacial variational form. We established a weak embedding inequality that is very useful in the weak finite…
The paper develops a hybrid method for solving a system of advection--diffusion equations in a bulk domain coupled to advection--diffusion equations on an embedded surface. A monotone nonlinear finite volume method for equations posed in…
We establish stable finite element (FE) approximations of convection-diffusion initial boundary value problems using the automatic variationally stable finite element (AVS-FE) method. The transient convection-diffusion problem leads to…
We study the heat equation on a half-space with a linear dynamical boundary condition. Our main aim is to show that, if the diffusion coefficient tends to infinity, then the solutions converge (in a suitable sense) to solutions of the…
The heat transfer characteristics of thin film flow over a hot sphere resulting from a cold vertical jet of liquid falling onto the surface has been investigated. The underlying physical features have been illustrated by numerical solutions…
In this chapter we consider different approximations for the one-dimensional one-phase Stefan problem corresponding to the fusion process of a semi-infinite material with a temperature boundary condition at the fixed face and non-linear…
We investigate the dependency of the magnitude of heat transfer in a convection cell as a function of its inclination by means of experiments and simulations. The study is performed with a working fluid of large Prandtl number, $Pr \simeq…
Long simulation times in climate sciences typically require coarse grids due to computational constraints. Nonetheless, unresolved subscale information significantly influences the prognostic variables and can not be neglected for reliable…
To assess the durability of structures, heat and moisture transport need to be analyzed. To provide a reliable estimation of heat and moisture distribution in a certain structure, one needs to include all available information about the…
Heat transfer by large deformable drops in a turbulent flow is a complex and rich in physics system, in which drops deformation, breakage and coalescence influence the transport of heat. We study this problem coupling direct numerical…
We investigate the influence of the thermal properties of the boundaries in turbulent Rayleigh-B\'enard convection on analytical upper bounds on convective heat transport. We model imperfectly conducting bounding plates in two ways: using…
We prove the existence of an eddy heat diffusion coefficient coming from an idealized model of turbulent fluid. A difficulty lies in the presence of a boundary, with also turbulent mixing and the eddy diffusion coefficient going to zero at…
In this paper, we consider a reaction-diffusion system describing the propagation of flames under the assumption of ignition-temperature kinetics and fractional reaction order. It was shown in [3] that this system admits a traveling front…