An Efficient Second-Order Accurate and Continuous Interpolation for Block-Adaptive Grids

TL;DR

This paper introduces a second-order, continuous interpolation algorithm for cell-centered AMR grids that enhances efficiency, maintains accuracy at resolution changes, and is suitable for parallel computing and applications like particle tracking and visualization.

Contribution

The paper presents a novel classification-based approach enabling efficient, second-order, continuous interpolation on AMR grids, addressing resolution change challenges and supporting parallel computation.

Findings

Efficient interpolation with second-order accuracy on AMR grids.

Maintains continuity and avoids false gradients at resolution interfaces.

Suitable for parallel processing and complex applications like particle tracking.

Abstract

In this paper we present a second-order and continuous interpolation algorithm for cell-centered adaptive-mesh-refinement (AMR) grids. Continuity requirement poses a non-trivial problem at resolution changes. We develop a classification of the resolution changes, which allows us to employ efficient and simple linear interpolation in the majority of the computational domain. The benefit of such approach is higher efficiency. The algorithm is well suited for massively parallel computations. Our interpolation algorithm allows extracting jump-free interpolated data distribution along lines and surfaces within the computational domain. This capability is important for various applications, including kinetic particles tracking in three dimensional vector fields, visualization (i.e. surface extraction) and extracting variables along one-dimensional curves such as field lines, streamlines and satellite trajectories, etc. Particular examples of the latter are models for acceleration of solar energetic particles (SEPs) along magnetic field-lines. As such models are sensitive to sharp gradients and discontinuities the capability to interpolate the data from the AMR grid to be passed to the SEP model without producing false gradients numerically becomes crucial. The code implementation of our algorithm is publicly available as a Fortran 90 library.