标题： WallGo有多快？ 用于计算一级相变壁速度的软件包 显示英文标题

标题： How fast does the WallGo? A package for computing wall velocities in first-order phase transitions

摘要： WallGo 是一种开源软件，用于计算一阶宇宙相变中的气泡壁速度，同时还计算引力波生成可用的能量预算。WallGo 的主要部分由 Python 编写，通过求解标量场（或多标量场）的运动方程、玻尔兹曼方程以及流体速度和温度的能量动量守恒，来确定壁的速度。WallGo 还包括两个辅助模块：WallGoMatrix，用于计算非平衡粒子的矩阵元；WallGoCollision，用于对玻尔兹曼碰撞项执行高维积分。 用户可以通过定义有效势并指定一组非平衡粒子及其相互作用来实现自定义模型。作为首个公开发布的计算包含非平衡贡献的壁速度的软件，WallGo 相较于早期计算中常见的假设，提高了计算精度。它采用谱方法处理偏离平衡和碰撞项，提供了基多项式的指数收敛，并支持多个非平衡粒子，允许玻尔兹曼混合项。WallGo 针对主导摩擦效应的非逃逸壁情景进行了优化设计。 本文介绍了该软件及其背后的理论基础，更详细的文档可在 https://wallgo.readthedocs.io 查阅。 显示英文摘要

摘要： WallGo is an open source software for the computation of the bubble wall velocity in first-order cosmological phase transitions. It also computes the energy budget available for the generation of gravitational waves. The main part of WallGo, built in Python, determines the wall velocity by solving the scalar-field(s) equation of motion, the Boltzmann equations and energy-momentum conservation for the fluid velocity and temperature. WallGo also includes two auxiliary modules: WallGoMatrix, which computes matrix elements for out-of-equilibrium particles, and WallGoCollision, which performs higher-dimensional integrals for Boltzmann collision terms. Users can implement custom models by defining an effective potential and specifying a list of out-of-equilibrium particles and their interactions. As the first public software to compute the wall velocity including out-of-equilibrium contributions, WallGo improves the precision of the computation compared to common assumptions in earlier computations. It utilises a spectral method for the deviation from equilibrium and collision terms that provides exponential convergence in basis polynomials, and supports multiple out-of-equilibrium particles, allowing for Boltzmann mixing terms. WallGo is tailored for non-runaway wall scenarios where leading-order coupling effects dominate friction. While this work introduces the software and the underlying theory, a more detailed documentation can be found in https://wallgo.readthedocs.io.