相关论文: Adjoint for advection schemes on the sphere in ICO…
The paper is concerned with an adjoint complement to the Volume-of-Fluid (VoF) method for immiscible two-phase flows, e.g. air and water, which is widely used in marine engineering due to its computational efficiency. The particular…
Implicit time-stepping for advection is applied locally in space and time where Courant numbers are large, but standard explicit time-stepping is used for the remaining solution which is typically the majority. This adaptively implicit…
It is of crucial importance to be able to identify the location of atmospheric pollution sources in our planet. Global models of atmospheric transport in combination with diverse Earth observing systems are a natural choice to achieve this…
Seismic traveltime tomography represents a popular and useful tool for unravelling the structure of the subsurface across the scales. In this work we address the case where the forward model is represented by the eikonal equation and derive…
We introduce Adjoint Sampling, a highly scalable and efficient algorithm for learning diffusion processes that sample from unnormalized densities, or energy functions. It is the first on-policy approach that allows significantly more…
We present a novel artificial diffusion method to circumvent the instabilities associated with the standard finite element approximation of convection-diffusion equations. Motivated by the micromorphic approach, we introduce an auxiliary…
This paper addresses the question whether there are numerical schemes for constant-coefficient advection problems that can yield convergent solutions for an infinite time horizon. The motivation is that such methods may serve as building…
In recent years, the use of adjoint vectors in Computational Fluid Dynamics (CFD) has seen a dramatic rise. Their utility in numerous applications, including design optimization, data assimilation, and mesh adaptation has sparked the…
This paper presents a novel adjoint solver for differentiable fluid simulation based on bidirectional flow maps. Our key observation is that the forward fluid solver and its corresponding backward, adjoint solver share the same flow map as…
This work focuses on numerically solving a shape identification problem related to advection-diffusion processes with space-dependent coefficients using shape optimization techniques. Two boundary-type cost functionals are considered, and…
In this paper we study a system of advection-diffusion equations in a bulk domain coupled to an advection-diffusion equation on an embedded surface. Such systems of coupled partial differential equations arise in, for example, the modeling…
The study of chaotic mixing is important for its potential to improve our understanding of fluid systems. Contour advection simulations provide a good model of the phenomenon by tracking the evolution of one or more contours or isolines of…
This article shows how to develop an efficient solver for a stabilized numerical space-time formulation of the advection-dominated diffusion transient equation. At the discrete space-time level, we approximate the solution by using…
In this research note we provide a variational basis for the optimal artificial diffusion method, which has been a cornerstone in developing many stabilized methods. The optimal artificial diffusion method produces exact nodal solutions…
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…
Boundary integral methods are attractive for solving homogeneous linear constant coefficient elliptic partial differential equations on complex geometries, since they can offer accurate solutions with a computational cost that is linear or…
We propose an alternative method for one-dimensional continuum diffusion models with spatially variable (heterogeneous) diffusivity. Our method, which extends recent work on stochastic diffusion, assumes the constant-coefficient homogenized…
This work focuses on the numerical assessment of the accuracy of an adjoint-based gradient in the perspective of variational data assimilation and parameter identification in glaciology. Using noisy synthetic data, we quantify the ability…
High fidelity simulations, e.g., large eddy simulation are often needed for accurately predicting pressure losses due to wake mixing in turbomachinery applications. An unsteady adjoint of such high fidelity simulations is useful for design…
In this paper, we propose high order numerical methods to solve a 2D advection diffusion equation, in the highly oscillatory regime. We use an integrator strategy that allows the construction of arbitrary high-order schemes {leading} to an…