차세대 리튬-황(Li-S) 배터리 폴리설파이드(LiPS) 셔틀 억제 & 1,000Hz 0-Alloc C# 반응-확산 편미분 전기화학 시뮬레이션 엔진

using System;
using System.Runtime.CompilerServices;

namespace ZeliDesk.Education.StemEnergy.LithiumSulfur
{
    public readonly record struct BatteryOperatingState(
        float CurrentDensityAcm2, // 충/방전 전류 밀도
        float TemperatureKelvin,
        float ElectrolyteViscosityCp,
        float SeparatorPorosity
    );

    public ref struct ShuttleTelemetry
    {
        public float ShuttleCurrentAcm2;
        public float CoulombicEfficiencyPercent;
        public float PolysulfideConcentrationAtAnodeMolar;
        public float CapacityRetentionPercent;
    }

    public static class LiSPolysulfideShuttleCore
    {
        private const int SpatialNodes = 16; // 음극-분리막-양극 1차원 공간 격자수
        private const float BaseDiffusivityCm2PerS = 1.5e-6f;
        private const float AnodeReactionRateConstant = 2.4e-3f; // cm/s
        private const float FaradayConstantF = 96485.33f;

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static void SimulateDiffusionStep(
            in BatteryOperatingState state,
            Span concentrationGrid, // 길이 16 스택 버퍼 (0-Alloc)
            float dtSec,
            ref ShuttleTelemetry telemetry)
        {
            if (concentrationGrid.Length < SpatialNodes) return;

            float dx = 0.005f / (SpatialNodes - 1); // 50 um 전해액 도메인 (cm)
            float effectiveDiffusivity = BaseDiffusivityCm2PerS * MathF.Pow(state.SeparatorPorosity, 1.5f);

            // 1. 유한차분 확산 방정식 스택 연산 (0-Alloc)
            Span tempNext = stackalloc float[SpatialNodes];
            concentrationGrid.CopyTo(tempNext);

            float rFactor = effectiveDiffusivity * dtSec / (dx * dx);

            for (int i = 1; i < SpatialNodes - 1; i++)
            {
                tempNext[i] = concentrationGrid[i] + rFactor * (concentrationGrid[i + 1] - 2f * concentrationGrid[i] + concentrationGrid[i - 1]);
            }

            // 2. 음극 경계조건: 리튬과의 기생 반응으로 소모
            float anodeConsumptionRate = AnodeReactionRateConstant * concentrationGrid[0] * dtSec / dx;
            tempNext[0] = MathF.Max(0f, concentrationGrid[0] + rFactor * (concentrationGrid[1] - concentrationGrid[0]) - anodeConsumptionRate);

            // 3. 양극 경계조건: 인가 전류에 비례하여 폴리설파이드 생성
            float generationRate = MathF.Abs(state.CurrentDensityAcm2) / (2f * FaradayConstantF) * 1e3f * dtSec / dx; // mol/cm^3
            tempNext[SpatialNodes - 1] = concentrationGrid[SpatialNodes - 1] + generationRate;

            tempNext.CopyTo(concentrationGrid);

            // 4. 셔틀 전류 및 쿨롱 효율 산출
            float shuttleCurrent = 2f * FaradayConstantF * AnodeReactionRateConstant * (concentrationGrid[0] * 1e-3f);
            telemetry.ShuttleCurrentAcm2 = shuttleCurrent;
            telemetry.PolysulfideConcentrationAtAnodeMolar = concentrationGrid[0];

            float loadCurrent = MathF.Max(1e-4f, MathF.Abs(state.CurrentDensityAcm2));
            telemetry.CoulombicEfficiencyPercent = Math.Clamp((loadCurrent - shuttleCurrent) / loadCurrent * 100f, 0f, 100f);
            telemetry.CapacityRetentionPercent = Math.Max(0f, 100f - shuttleCurrent * 50f);
        }
    }
}