Related papers: Numerical Considerations for Advection-Diffusion P…
We study reaction-diffusion equations in cylinders with possibly nonlinear diffusion and possibly nonlinear Neumann boundary conditions. We provide a geometric Poincar\'e-type inequality and classification results for stable solutions, and…
Computational fluid dynamics (CFD) is increasingly used to study blood flows in patient-specific arteries for understanding certain cardiovascular diseases. The techniques work quite well for relatively simple problems, but need…
In this article, we are concerned with the analysis on the numerical reconstruction of the spatial component in the source term of a time-fractional diffusion equation. This ill-posed problem is solved through a stabilized nonlinear…
This paper presents a formulation of the reactive dynamic user equilibrium problem in continuum form using a network-level Macroscopic Fundamental Diagram (MFD). Compared to existing continuum models for cities -- all based in Hughes'…
Real-world flow applications in complex scientific and engineering domains, such as geosciences, challenge classical simulation methods due to large spatial domains, high spatio-temporal resolution requirements, and potentially strong…
Numerical underflow and overflow are major hurdles for rolling-out the modeling and simulation infrastructure for temperatures below about 50 K. Extending the numeric precision is computationally intensive and thus best avoided. The root…
In order to prevent velocity, pressure, and temperature spikes at material discontinuities occurring when the interface-capturing schemes inconsistently simulate compressible multi-material flows(when the specific heats ratio is…
In this paper, we introduce a new conservation-based approach to model traffic dynamics, and apply the model predictive control (MPC) approach to control the boundary traffic inflow and outflow, so that the traffic congestion is reduced. We…
The article discusses the gradient discretisation method (GDM) for distributed optimal control problems governed by diffusion equation with pure Neumann boundary condition. Using the GDM framework enables to develop an analysis that…
One approach to reduce the cost to simulate transitional compressible boundary layer flow is to adopt a near body reduced domain with boundary conditions enforced to be compatible with a computationally cheaper 3D RANS simulation. In such…
We propose an efficient numerical strategy for simulating fluid flow through porous media with highly oscillatory characteristics. Specifically, we consider non-linear diffusion models. This scheme is based on the classical homogenization…
Computational gas dynamics has become a prominent research field both in astrophysics and cosmology. In the first part of this review we intend to briefly describe several of the numerical methods used in this field, discuss their range of…
This paper is concerned with the numerical solution of porous-media flow and transport problems , i. e. heterogeneous, advection-diffusion problems. Its aim is to investigate numerical schemes for these problems in which different time…
Two-phase outflows refer to situations where the interface formed between two immiscible incompressible fluids passes through open portions of the domain boundary. We present in this paper several new forms of open boundary conditions for…
We present a novel mathematical model that simulates myocardial blood perfusion by embedding multiscale and multiphysics features. Our model incorporates cardiac electrophysiology, active and passive mechanics, hemodynamics, reduced valve…
This paper analyzes the stability of a reactiondiffusion equation coupled with a finite-dimensional controller through Dirichlet boundary input and Neumann boundary output. Going against the flow, we intend to propose numerical certificates…
I previously used Burgers' equation to introduce a new method of numerical discretisation of \pde{}s. The analysis is based upon centre manifold theory so we are assured that the discretisation accurately models all the processes and their…
Compressible interfacial multiphase flows (CIMF) are essential to different applications, such as liquid fuel injection in supersonic propulsion systems. Since high-level details in CIMF are often difficult to measure in experiments,…
We report the key findings from numerical solutions of a model of transport within an established perfusion bioreactor design. The model includes a complete formulation of transport with fully coupled convection-diffusion and scaffold cell…
The increasing application of cardiorespiratory simulations for diagnosis and surgical planning necessitates the development of computational methods significantly faster than the current technology. To achieve this objective, we leverage…