advectionDiffusion1D.js

/**
 * ════════════════════════════════════════════════════════════════
 *  FEAScript Core Library
 *  Lightweight Finite Element Simulation in JavaScript
 *  Version: 0.3.0 (RC) | https://feascript.com
 *  MIT License © 2023–2026 FEAScript
 * ════════════════════════════════════════════════════════════════
 */

// Import Math.js
import * as math from "mathjs";
global.math = math;

// Import FEAScript library
import { FEAScriptModel, printVersion } from "feascript";

console.log("FEAScript Version:", printVersion);

// Create a new FEAScript model
const model = new FEAScriptModel();

// Select physics/PDE
model.setModelConfig("generalFormPDEScript", {
  coefficientFunctions: {
    // Equation d²u/dx² - 10 du/dx = 10 * exp(-200 * (x - 0.5)²)
    A: (x) => 1, // Diffusion coefficient
    B: (x) => -10, // Advection coefficient
    C: (x) => 0, // Reaction coefficient
    D: (x) => 10 * Math.exp(-200 * Math.pow(x - 0.5, 2)), // Source term
  },
});

// Define mesh configuration
model.setMeshConfig({
  meshDimension: "1D",
  elementOrder: "quadratic",
  numElementsX: 20,
  maxX: 1.0,
});

// Define boundary conditions
model.addBoundaryCondition("0", ["constantValue", 1]); // Left boundary
model.addBoundaryCondition("1", "zeroGradient"); // Right boundary

// Set solver method
model.setSolverMethod("lusolve");

// Solve the problem
const { solutionVector, nodesCoordinates } = model.solve();

// Print results
console.log(`Number of nodes in mesh: ${nodesCoordinates.nodesXCoordinates.length}`);
console.log("Node coordinates:", nodesCoordinates);
console.log("Solution vector:", solutionVector);