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Exponential integrators have been introduced as an efficient alternative to explicit and implicit methods for integrating large stiff systems of differential equations. Over the past decades these methods have been studied theoretically and…

In this paper we propose a novel class of methods for high order accurate integration of multirate systems of ordinary differential equation initial-value problems. The proposed methods construct multirate schemes by approximating the…

In this paper, we present a multiscale method for simulations of the multicontinua unsaturated flow problems in heterogeneous fractured porous media. The mathematical model is described by the system of Richards equations for each continuum…

Numerical simulations of two-phase flow and fluid structure interaction problems are of great interest in many environmental problems and engineering applications. To capture the complex physical processes involved in these problems, a high…

Computational studies that use block-structured adaptive mesh refinement (AMR) approaches suffer from unnecessarily high mesh resolution in regions adjacent to important solution features. This deficiency limits the performance of AMR…

We present a new solver for massively parallel simulations of fully three-dimensional multiphase flows. The solver runs on a variety of computer architectures from laptops to supercomputers and on 65536 threads or more (limited only by the…

Traditional time discretization methods use a single timestep for the entire system of interest and can perform poorly when the dynamics of the system exhibits a wide range of time scales. Multirate infinitesimal step (MIS) methods (Knoth…

A multigrid scheme is proposed for the pressure equation of the incompressible unsteady fluid flow equations, allowing efficient implementation on clusters of modern CPUs, many integrated core devices (MICs), and graphics processing units…

Triply Periodic Minimal Surface (TPMS) structures have emerged as a new class of porous materials with variable geometries and favourable transport properties, making them promising for reactor internals in chemical engineering. However,…

We investigate a multirate time step approach applied to decoupled methods in fluid and structure interaction(FSI) computation, where two different time steps are used for fluid and structure respectively. For illustration, the multirate…

In this paper, we propose a multirate iterative scheme with multiphysics finite element method for a fluid-saturated poroelasticity model. Firstly, we reformulate the original model into a fluid coupled problem to apply the multiphysics…

Understanding grain-surface processes is crucial to interpreting the chemistry of the ISM. However, accurate surface chemistry models are computationally expensive and are difficult to integrate with gas-phase simulations. A new…

Standard gradient-based iteration algorithms for optimization, such as gradient descent and its various proximal-based extensions to nonsmooth problems, are known to converge slowly for ill-conditioned problems, sometimes requiring many…

Stabilized explicit methods are particularly efficient for large systems of stiff stochastic differential equations (SDEs) due to their extended stability domain. However, they loose their efficiency when a severe stiffness is induced by…

Explicit stabilized methods are highly efficient time integrators for large and stiff systems of ordinary differential equations especially when applied to semi-discrete parabolic problems. However, when local spatial mesh refinement is…

High-order discretizations of partial differential equations (PDEs) necessitate high-order time integration schemes capable of handling both stiff and nonstiff operators in an efficient manner. Implicit-explicit (IMEX) integration based on…

In this work, we build upon the recently introduced Multiscale Robin Coupled Method with Oversampling and Smoothing (MRCM-OS) to develop two highly efficient iterative multiscale methods. The MRCM-OS methodology demonstrated the ability to…

We present a cross-architecture high-order heterogeneous Navier-Stokes simulation solver, XFluids, for compressible reacting multicomponent flows on different platforms. The multi-component reacting flows are ubiquitous in many scientific…

High-speed chemically active flows present significant computational challenges due to their disparate space and time scales, where stiff chemistry often dominates simulation time. While modern supercomputing scientific codes achieve…

This paper considers flow problems in multiscale heterogeneous porous media. The multiscale nature of the modeled process significantly complicates numerical simulations due to the need to compute huge and ill-conditioned sparse matrices,…