In this work we aim at developing a new class of high order accurate well-balanced finite difference (FD) Weighted Essentially Non-Oscillatory (WENO) methods for numerical general relativity, which can be applied to any first--order reduction of the Einstein field equations, even if non--conservative terms are present. We choose the first--order non--conservative Z4 formulation of the Einstein equations, which has a built--in cleaning procedure that accounts for the Einstein constraints and that has already shown its ability in keeping stationary solutions stable over long timescales. Upon the introduction of auxiliary variables, the vacuum Einstein equations in first order form constitute a ...

翻译：本文旨在发展一类适用于数值广义相对论的高阶精度保平衡有限差分加权本质无振荡方法，该方法可应用于爱因斯坦场方程的任何一阶约化形式，即使存在非守恒项。我们选择一阶非守恒Z4形式下的爱因斯坦方程，该形式内置了处理爱因斯坦约束条件的清理程序，并已证明其能在长时间尺度上保持稳态解的稳定性。通过引入辅助变量，一阶形式的真空爱因斯坦方程构成了一个...