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Added some new physics/maths classes: Temperature, Pressure, WaterPhaseCalculator.
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‎modules/squarepine_core/maths/Pressure.h‎

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/** A simple class to represent a pressure.
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Internally, this is stored in Pascals, and it can be converted
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to and from a variety of common pressure units.
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*/
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class Pressure
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{
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public:
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/** Default constructor, which sets the instance to 101325 Pa. */
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Pressure() noexcept = default;
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/** Copy constructor. */
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Pressure (const Pressure&) noexcept = default;
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/** Move constructor. */
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Pressure (Pressure&&) noexcept = default;
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/** Destructor. */
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~Pressure() noexcept = default;
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/** Constructor that initialises the pressure with a value in Pascals. */
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explicit constexpr Pressure (double initialPascals) noexcept : pascals (initialPascals) {}
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/** Copy-assignment operator */
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Pressure& operator= (const Pressure&) noexcept = default;
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/** Move-assignment operator */
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Pressure& operator= (Pressure&&) noexcept = default;
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//==============================================================================
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/** @returns the value in Pascals. */
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constexpr double get() const noexcept { return pascals; }
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/** @returns the value in kPa. */
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constexpr double toKiloPascals() const noexcept { return pascals / 1000.0; }
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/** @returns the value in mmHg. */
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constexpr double toMillimetersHg() const noexcept { return pascals * 0.00750062; }
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/** @returns the value in atm. */
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constexpr double toAtmospheres() const noexcept { return pascals / 101325.0; }
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/** @returns the value in bar. */
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constexpr double toBar() const noexcept { return pascals / 100000.0; }
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/** @returns the value in PSI. */
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constexpr double toPSI() const noexcept { return pascals * 0.000145038; }
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//==============================================================================
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/** @returns a pressure value in Pascals from the provided pressure in kPa. */
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static Pressure fromKiloPascals (double value) noexcept { return Pressure (value * 1000.0); }
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/** @returns a pressure value in Pascals from the provided pressure in mmHg. */
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static Pressure fromMillimetersHg (double value) noexcept { return Pressure (value * 133.322); }
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/** @returns a pressure value in Pascals from the provided pressure in atm. */
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static Pressure fromAtmospheres (double value) noexcept { return Pressure (value * 101325.0); }
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/** @returns a pressure value in Pascals from the provided pressure in bar. */
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static Pressure fromBar (double value) noexcept { return Pressure (value * 100000.0); }
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/** @returns a pressure value in Pascals from the provided pressure in PSI. */
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static Pressure fromPSI (double value) noexcept { return Pressure (value * 6894.76); }
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private:
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//==============================================================================
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double pascals = 101325.0;
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};

‎modules/squarepine_core/maths/Temperature.h‎

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/** A simple class to represent a temperature.
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Internally, this is stored in Celsius, and it can be converted
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to and from a variety of common temperature units.
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*/
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class Temperature
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{
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public:
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/** Default constructor, which sets the instance to 0 degrees Celsius. */
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Temperature() noexcept = default;
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/** Copy constructor. */
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Temperature (const Temperature&) noexcept = default;
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/** Move constructor. */
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Temperature (Temperature&&) noexcept = default;
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/** Destructor. */
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~Temperature() noexcept = default;
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/** Constructor that initialises the temperature with a value in Celsius. */
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explicit Temperature (double initialCelsius) noexcept : celsius (initialCelsius) {}
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/** Copy-assignment operator */
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Temperature& operator= (const Temperature&) noexcept = default;
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/** Move-assignment operator */
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Temperature& operator= (Temperature&&) noexcept = default;
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//==============================================================================
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/** @returns the value in Celsius. */
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constexpr double get() const noexcept { return celsius; }
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/** @returns the value in Fahrenheit. */
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constexpr double toFahrenheit() const noexcept { return (celsius * 9.0 / 5.0) + 32.0; }
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/** @returns the value in Kelvin. */
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constexpr double toKelvin() const noexcept { return celsius + 273.15; }
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/** @returns a temperature value in Celsius from the provided Fahrenheit temperature. */
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static Temperature fromFahrenheit (double value) noexcept { return Temperature ((value - 32.0) * 5.0 / 9.0); }
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/** @returns a temperature value in Celsius from the provided Kelvin temperature. */
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static Temperature fromKelvin (double value) noexcept { return Temperature (value - 273.15); }
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private:
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//==============================================================================
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double celsius = 0.0;
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};

‎modules/squarepine_core/maths/WaterPhaseCalculator.h‎

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/** The phase of water. */
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enum class WaterPhase
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{
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solid,
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liquid,
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gas,
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supercritical
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};
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/** @returns the String representation of the given water's phase. */
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inline String toString (WaterPhase mp) noexcept
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{
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switch (mp)
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{
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case WaterPhase::solid: return TRANS ("Solid");
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case WaterPhase::liquid: return TRANS ("Liquid");
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case WaterPhase::gas: return TRANS ("Gas");
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case WaterPhase::supercritical: return TRANS ("Supercritical Fluid");
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default: return TRANS ("Unknown");
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}
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}
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class WaterPhaseCalculator final
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{
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public:
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/** Freezing point (°C) correlated with pressure (Pa). */
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static double getFreezingPointCelsius (double pressurePa)
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{
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constexpr auto slope = -7.4e-8; // K/Pa near 1 atm
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constexpr auto Pref = kPaPerAtm;
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constexpr auto TrefC = 0.0;
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return TrefC + slope * (pressurePa - Pref);
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}
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/** Boiling point (°C) vs pressure (Pa) using Wagner correlation. */
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static std::optional<double> getBoilingPointCelsius (double pressurePa,
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double tolK = 1e-5,
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int maxIters = 100)
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{
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if (pressurePa < Ptriple || pressurePa >= Pc)
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return std::nullopt;
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auto lo = Ttriple;
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auto hi = Tc - 1e-6;
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auto PloOpt = saturationPressurePa_Wagner (lo);
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auto PhiOpt = saturationPressurePa_Wagner (hi);
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if (!PloOpt || !PhiOpt)
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return std::nullopt;
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auto Plo = *PloOpt;
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auto Phi = *PhiOpt;
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if (!(Plo <= pressurePa && pressurePa <= Phi))
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return std::nullopt;
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for (int i = 0; i < maxIters && (hi - lo) > tolK; ++i)
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{
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auto mid = 0.5 * (lo + hi);
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auto PmidOpt = saturationPressurePa_Wagner(mid);
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if (!PmidOpt)
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return std::nullopt;
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auto Pmid = *PmidOpt;
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if (Pmid < pressurePa) lo = mid;
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else hi = mid;
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}
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const auto T_K = 0.5 * (lo + hi);
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return T_K - 273.15;
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}
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/** Phase determination. */
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static WaterPhase getWaterPhase (double tempC, double pressurePa)
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{
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if (pressurePa < Ptriple)
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return (tempC < (Ttriple - 273.15))
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? WaterPhase::solid
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: WaterPhase::gas;
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if (pressurePa >= Pc && (tempC + 273.15) >= Tc)
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return WaterPhase::supercritical;
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const auto TfC = getFreezingPointCelsius (pressurePa);
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if (tempC < TfC)
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return WaterPhase::solid;
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const auto TbOpt = getBoilingPointCelsius (pressurePa);
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if (!TbOpt)
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return (tempC >= (Tc - 273.15))
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? WaterPhase::supercritical
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: WaterPhase::liquid;
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if (tempC < *TbOpt)
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return WaterPhase::liquid;
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return WaterPhase::gas;
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}
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private:
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static inline constexpr double kPaPerAtm = 101325.0;
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static inline constexpr double Tc = 647.096; // K
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static inline constexpr double Pc = 22.064e6; // Pa
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static inline constexpr double Ttriple = 273.16; // K
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static inline constexpr double Ptriple = 611.657; // Pa
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/** Wagner saturation pressure. */
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static std::optional<double> saturationPressurePa_Wagner (double T_K)
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{
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if (T_K < Ttriple || T_K > Tc)
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return std::nullopt;
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constexpr auto a = -7.85951783;
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constexpr auto b = 1.84408259;
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constexpr auto c = -11.7866497;
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constexpr auto d = 22.6807411;
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constexpr auto e = -15.9618719;
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constexpr auto f = 1.80122502;
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auto tau = 1.0 - T_K / Tc;
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auto poly = a * tau
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+ b * std::pow (tau, 1.5)
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+ c * std::pow (tau, 3.0)
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+ d * std::pow (tau, 3.5)
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+ e * std::pow (tau, 4.0)
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+ f * std::pow (tau, 7.5);
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const auto lnPratio = (Tc / T_K) * poly;
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return Pc * std::exp (lnPratio);
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}
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};

‎modules/squarepine_core/squarepine_core.h‎

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#include "maths/Polynomials.h"
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#include "maths/Steps.h"
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#include "maths/Vector4D.h"
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#include "maths/Pressure.h"
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#include "maths/Temperature.h"
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#include "maths/WaterPhaseCalculator.h"
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#include "memory/Allocator.h"
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#include "misc/Amalgamator.h"
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#include "misc/ArrayIterationUnroller.h"

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