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For Hamiltonian systems, simulation algorithms that exactly conserve numerical energy or pseudo-energy have seen extensive investigation. Most available methods either require the iterative solution of nonlinear algebraic equations at each…

The choice of numerical integrator in approximating solutions to dynamic partial differential equations depends on the smallest time-scale of the problem at hand. Large-scale deformations in elastic solids contain both shear waves and bulk…

Plastic deformation of most crystalline materials is due to the motion of lattice dislocations. Therefore, the simulation of the interaction and dynamics of these defects has become state-of-the-art method to study work hardening, size…

We study three different time integration methods for a dynamic pore network model for immiscible two-phase flow in porous media. Considered are two explicit methods, the forward Euler and midpoint methods, and a new semi-implicit method…

There are various situations where the classical Fourier's law for heat conduction is not applicable, such as heat conduction in heterogeneous materials or for modeling low-temperature phenomena. In such cases, heat flux is not directly…

Innovative numerical scheme studied in this work enables to overcome two main limitations of Building Performance Simulation (BPS) programs as high computational cost and the choice of a very fine numerical grid. The method, called…

Nonlinear time fractional partial differential equations are widely used in modeling and simulations. In many applications, there are high contrast changes in media properties. For solving these problems, one often uses coarse spatial grid…

This work proposes an extension of phase change and latent heat models for the simulation of metal powder bed fusion additive manufacturing processes on the macroscale and compares different models with respect to accuracy and numerical…

Solving multiscale diffusion problems is often computationally expensive due to the spatial and temporal discretization challenges arising from high-contrast coefficients. To address this issue, a partially explicit temporal splitting…

The numerical simulation of fluid flow through a complex geometry with heat transfer is of strong interest for many applications, such as oil-filled power transformers. A fundamental challenge here is that high resolution is necessary to…

This paper presents a multiscale methodology for efficient unsteady conjugate heat transfer simulations. The solid domain is modelled by coupling a global representation of the temperature field, based on the eigenfunctions of the unsteady…

Two phase flows that include phase transition, especially phase creation, with a sharp interface remain a challenging task for numerics. We consider the isothermal Euler equations with phase transition between a liquid and a vapor phase.…

We present an implicit-explicit finite volume scheme for two-fluid single-temperature flow in all Mach number regimes which is based on a symmetric hyperbolic thermodynamically compatible description of the fluid flow. The scheme is stable…

Comparisons of experimental observation of heat and moisture transfer through porous building materials with numerical results have been presented in numerous studies reported in literature. However, some discrepancies have been observed,…

For time-dependent problems with high-contrast multiscale coefficients, the time step size for explicit methods is affected by the magnitude of the coefficient parameter. With a suitable construction of multiscale space, one can achieve a…

Heat transfer simulations of the fused filament fabrication process are an important tool to predict bonding, residual stresses and strength of 3D printed parts. But in order to capture the significant thermal gradients that occur in the…

This study proposes a high-order multi-scale method tailored for time-dependent nonlinear thermo-electro-mechanical coupling problems of composite structures with highly spatial heterogeneity, which incorporate temperature-dependent…

In this work, we present an efficient approach to solve nonlinear high-contrast multiscale diffusion problems. We incorporate the explicit-implicit-null (EIN) method to separate the nonlinear term into a linear term and a damping term, and…

A new horizontally explicit/vertically implicit (HEVI) time splitting scheme for atmospheric modelling is introduced, for which the horizontal divergence terms are applied within the implicit vertical substep. The new HEVI scheme is…

Simulating physical problems involving multi-time scale coupling is challenging due to the need of solving these multi-time scale processes simultaneously. In response to this challenge, this paper proposed an explicit multi-time step…