如何在Vue Vuetify中使用单个添加节点按钮添加treeview节点？

<template>
  <div>
    <v-treeview :items="treeData"></v-treeview>
    <v-btn @click="addNode">添加节点</v-btn>
  </div>
</template>

<script>
export default {
  data() {
    return {
      treeData: [
        {
          id: 1,
          name: '节点1',
          children: [
            {
              id: 11,
              name: '子节点1'
            },
            {
              id: 12,
              name: '子节点2'
            }
          ]
        },
        {
          id: 2,
          name: '节点2'
        }
      ]
    };
  },
  methods: {
    addNode() {
      const newNode = {
        id: 3,
        name: '新节点'
      };
      this.treeData.push(newNode);
    }
  }
};
</script>