xref: /libCEED/examples/fluids/qfunctions/blasius.h (revision ea61e9ac44808524e4667c1525a05976f536c19c)

// Copyright (c) 2017-2022, Lawrence Livermore National Security, LLC and other CEED contributors.
// All Rights Reserved. See the top-level LICENSE and NOTICE files for details.
//
// SPDX-License-Identifier: BSD-2-Clause
//
// This file is part of CEED:  http://github.com/ceed

/// @file
/// Operator for Navier-Stokes example using PETSc

#ifndef blasius_h
#define blasius_h

#include <ceed.h>

#include "newtonian_state.h"
#include "newtonian_types.h"
#include "utils.h"

#define BLASIUS_MAX_N_CHEBYSHEV 50

typedef struct BlasiusContext_ *BlasiusContext;
struct BlasiusContext_ {
  bool                             implicit;                              // !< Using implicit timesteping or not
  bool                             weakT;                                 // !< flag to set Temperature weakly at inflow
  CeedScalar                       delta0;                                // !< Boundary layer height at inflow
  CeedScalar                       U_inf;                                 // !< Velocity at boundary layer edge
  CeedScalar                       T_inf;                                 // !< Temperature at boundary layer edge
  CeedScalar                       T_wall;                                // !< Temperature at the wall
  CeedScalar                       P0;                                    // !< Pressure at outflow
  CeedScalar                       x_inflow;                              // !< Location of inflow in x
  CeedScalar                       n_cheb;                                // !< Number of Chebyshev terms
  CeedScalar                      *X;                                     // !< Chebyshev polynomial coordinate vector (CPU only)
  CeedScalar                       eta_max;                               // !< Maximum eta in the domain
  CeedScalar                       Tf_cheb[BLASIUS_MAX_N_CHEBYSHEV];      // !< Chebyshev coefficient for f
  CeedScalar                       Th_cheb[BLASIUS_MAX_N_CHEBYSHEV - 1];  // !< Chebyshev coefficient for h
  struct NewtonianIdealGasContext_ newtonian_ctx;
};

// *****************************************************************************
// This helper function evaluates Chebyshev polynomials with a set of coefficients with all their derivatives represented as a recurrence table.
// *****************************************************************************
CEED_QFUNCTION_HELPER void ChebyshevEval(int N, const double *Tf, double x, double eta_max, double *f) {
  double dX_deta     = 2 / eta_max;
  double table[4][3] = {
  // Chebyshev polynomials T_0, T_1, T_2 of the first kind in (-1,1)
      {1, x, 2 * x * x - 1},
      {0, 1, 4 * x        },
      {0, 0, 4            },
      {0, 0, 0            }
  };
  for (int i = 0; i < 4; i++) {
    // i-th derivative of f
    f[i] = table[i][0] * Tf[0] + table[i][1] * Tf[1] + table[i][2] * Tf[2];
  }
  for (int i = 3; i < N; i++) {
    // T_n(x) = 2xT_{n-1}(x) - T_{n-2}(x)
    table[0][i % 3] = 2 * x * table[0][(i - 1) % 3] - table[0][(i - 2) % 3];
    // Differentiate Chebyshev polynomials with the recurrence relation
    for (int j = 1; j < 4; j++) {
      // T'_{n}(x)/n = 2T_{n-1}(x) + T'_{n-2}(x)/n-2
      table[j][i % 3] = i * (2 * table[j - 1][(i - 1) % 3] + table[j][(i - 2) % 3] / (i - 2));
    }
    for (int j = 0; j < 4; j++) {
      f[j] += table[j][i % 3] * Tf[i];
    }
  }
  for (int i = 1; i < 4; i++) {
    // Transform derivatives from Chebyshev [-1, 1] to [0, eta_max].
    for (int j = 0; j < i; j++) f[i] *= dX_deta;
  }
}

// *****************************************************************************
// This helper function computes the Blasius boundary layer solution.
// *****************************************************************************
State CEED_QFUNCTION_HELPER(BlasiusSolution)(const BlasiusContext blasius, const CeedScalar x[3], const CeedScalar x0, const CeedScalar x_inflow,
                                             const CeedScalar rho_infty, CeedScalar *t12) {
  CeedInt    N     = blasius->n_cheb;
  CeedScalar mu    = blasius->newtonian_ctx.mu;
  CeedScalar nu    = mu / rho_infty;
  CeedScalar eta   = x[1] * sqrt(blasius->U_inf / (nu * (x0 + x[0] - x_inflow)));
  CeedScalar X     = 2 * (eta / blasius->eta_max) - 1.;
  CeedScalar U_inf = blasius->U_inf;
  CeedScalar Rd    = GasConstant(&blasius->newtonian_ctx);

  CeedScalar f[4], h[4];
  ChebyshevEval(N, blasius->Tf_cheb, X, blasius->eta_max, f);
  ChebyshevEval(N - 1, blasius->Th_cheb, X, blasius->eta_max, h);

  *t12 = mu * U_inf * f[2] * sqrt(U_inf / (nu * (x0 + x[0] - x_inflow)));

  CeedScalar Y[5];
  Y[1] = U_inf * f[1];
  Y[2] = 0.5 * sqrt(nu * U_inf / (x0 + x[0] - x_inflow)) * (eta * f[1] - f[0]);
  Y[3] = 0.;
  Y[4] = blasius->T_inf * h[0];
  Y[0] = rho_infty / h[0] * Rd * Y[4];
  return StateFromY(&blasius->newtonian_ctx, Y, x);
}

// *****************************************************************************
// This QFunction sets a Blasius boundary layer for the initial condition
// *****************************************************************************
CEED_QFUNCTION(ICsBlasius)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
  // Inputs
  const CeedScalar(*X)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0];

  // Outputs
  CeedScalar(*q0)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0];

  const BlasiusContext context    = (BlasiusContext)ctx;
  const CeedScalar     cv         = context->newtonian_ctx.cv;
  const CeedScalar     mu         = context->newtonian_ctx.mu;
  const CeedScalar     T_inf      = context->T_inf;
  const CeedScalar     P0         = context->P0;
  const CeedScalar     delta0     = context->delta0;
  const CeedScalar     U_inf      = context->U_inf;
  const CeedScalar     x_inflow   = context->x_inflow;
  const CeedScalar     gamma      = HeatCapacityRatio(&context->newtonian_ctx);
  const CeedScalar     e_internal = cv * T_inf;
  const CeedScalar     rho        = P0 / ((gamma - 1) * e_internal);
  const CeedScalar     x0         = U_inf * rho / (mu * 25 / (delta0 * delta0));
  CeedScalar           t12;

  // Quadrature Point Loop
  CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
    const CeedScalar x[3] = {X[0][i], X[1][i], 0.};
    State            s    = BlasiusSolution(context, x, x0, x_inflow, rho, &t12);
    CeedScalar       q[5] = {0};
    UnpackState_U(s.U, q);
    for (CeedInt j = 0; j < 5; j++) q0[j][i] = q[j];

  }  // End of Quadrature Point Loop
  return 0;
}

// *****************************************************************************
CEED_QFUNCTION(Blasius_Inflow)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
  // Inputs
  const CeedScalar(*q)[CEED_Q_VLA]          = (const CeedScalar(*)[CEED_Q_VLA])in[0];
  const CeedScalar(*q_data_sur)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[2];
  const CeedScalar(*X)[CEED_Q_VLA]          = (const CeedScalar(*)[CEED_Q_VLA])in[3];

  // Outputs
  CeedScalar(*v)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0];

  const BlasiusContext     context  = (BlasiusContext)ctx;
  const bool               implicit = context->implicit;
  NewtonianIdealGasContext gas      = &context->newtonian_ctx;
  const CeedScalar         mu       = context->newtonian_ctx.mu;
  const CeedScalar         Rd       = GasConstant(&context->newtonian_ctx);
  const CeedScalar         T_inf    = context->T_inf;
  const CeedScalar         P0       = context->P0;
  const CeedScalar         delta0   = context->delta0;
  const CeedScalar         U_inf    = context->U_inf;
  const CeedScalar         x_inflow = context->x_inflow;
  const bool               weakT    = context->weakT;
  const CeedScalar         rho_0    = P0 / (Rd * T_inf);
  const CeedScalar         x0       = U_inf * rho_0 / (mu * 25 / Square(delta0));

  // Quadrature Point Loop
  CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
    // Setup
    // -- Interp-to-Interp q_data
    // For explicit mode, the surface integral is on the RHS of ODE q_dot = f(q).
    // For implicit mode, it gets pulled to the LHS of implicit ODE/DAE g(q_dot, q).
    // We can effect this by swapping the sign on this weight
    const CeedScalar wdetJb = (implicit ? -1. : 1.) * q_data_sur[0][i];

    // Calculate inflow values
    const CeedScalar x[3] = {X[0][i], X[1][i], 0.};
    CeedScalar       t12;
    State            s = BlasiusSolution(context, x, x0, x_inflow, rho_0, &t12);
    CeedScalar       qi[5];
    for (CeedInt j = 0; j < 5; j++) qi[j] = q[j][i];
    State s_int = StateFromU(gas, qi, x);

    // enabling user to choose between weak T and weak rho inflow
    if (weakT) {  // density from the current solution
      s.U.density = s_int.U.density;
      s.Y         = StatePrimitiveFromConservative(gas, s.U, x);
    } else {  // Total energy from current solution
      s.U.E_total = s_int.U.E_total;
      s.Y         = StatePrimitiveFromConservative(gas, s.U, x);
    }

    // ---- Normal vect
    const CeedScalar norm[3] = {q_data_sur[1][i], q_data_sur[2][i], q_data_sur[3][i]};

    StateConservative Flux_inviscid[3];
    FluxInviscid(&context->newtonian_ctx, s, Flux_inviscid);

    const CeedScalar stress[3][3] = {
        {0,   t12, 0},
        {t12, 0,   0},
        {0,   0,   0}
    };
    const CeedScalar Fe[3] = {0};  // TODO: viscous energy flux needs grad temperature
    CeedScalar       Flux[5];
    FluxTotal_Boundary(Flux_inviscid, stress, Fe, norm, Flux);
    for (CeedInt j = 0; j < 5; j++) v[j][i] = -wdetJb * Flux[j];
  }  // End Quadrature Point Loop
  return 0;
}

// *****************************************************************************
CEED_QFUNCTION(Blasius_Inflow_Jacobian)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
  // Inputs
  const CeedScalar(*dq)[CEED_Q_VLA]         = (const CeedScalar(*)[CEED_Q_VLA])in[0];
  const CeedScalar(*q_data_sur)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[2];
  const CeedScalar(*X)[CEED_Q_VLA]          = (const CeedScalar(*)[CEED_Q_VLA])in[3];

  // Outputs
  CeedScalar(*v)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0];

  const BlasiusContext context  = (BlasiusContext)ctx;
  const bool           implicit = context->implicit;
  const CeedScalar     mu       = context->newtonian_ctx.mu;
  const CeedScalar     cv       = context->newtonian_ctx.cv;
  const CeedScalar     Rd       = GasConstant(&context->newtonian_ctx);
  const CeedScalar     gamma    = HeatCapacityRatio(&context->newtonian_ctx);
  const CeedScalar     T_inf    = context->T_inf;
  const CeedScalar     P0       = context->P0;
  const CeedScalar     delta0   = context->delta0;
  const CeedScalar     U_inf    = context->U_inf;
  const bool           weakT    = context->weakT;
  const CeedScalar     rho_0    = P0 / (Rd * T_inf);
  const CeedScalar     x0       = U_inf * rho_0 / (mu * 25 / (delta0 * delta0));

  // Quadrature Point Loop
  CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
    // Setup
    // -- Interp-to-Interp q_data
    // For explicit mode, the surface integral is on the RHS of ODE q_dot = f(q).
    // For implicit mode, it gets pulled to the LHS of implicit ODE/DAE g(q_dot, q).
    // We can effect this by swapping the sign on this weight
    const CeedScalar wdetJb = (implicit ? -1. : 1.) * q_data_sur[0][i];

    // Calculate inflow values
    const CeedScalar x[3] = {X[0][i], X[1][i], X[2][i]};
    CeedScalar       t12;
    State            s = BlasiusSolution(context, x, x0, 0, rho_0, &t12);

    // enabling user to choose between weak T and weak rho inflow
    CeedScalar drho, dE, dP;
    if (weakT) {
      // rho should be from the current solution
      drho                   = dq[0][i];
      CeedScalar dE_internal = drho * cv * T_inf;
      CeedScalar dE_kinetic  = .5 * drho * Dot3(s.Y.velocity, s.Y.velocity);
      dE                     = dE_internal + dE_kinetic;
      dP                     = drho * Rd * T_inf;  // interior rho with exterior T
    } else {                                       // rho specified, E_internal from solution
      drho = 0;
      dE   = dq[4][i];
      dP   = dE * (gamma - 1.);
    }
    const CeedScalar norm[3] = {q_data_sur[1][i], q_data_sur[2][i], q_data_sur[3][i]};

    const CeedScalar u_normal = Dot3(norm, s.Y.velocity);

    v[0][i] = -wdetJb * drho * u_normal;
    for (int j = 0; j < 3; j++) {
      v[j + 1][i] = -wdetJb * (drho * u_normal * s.Y.velocity[j] + norm[j] * dP);
    }
    v[4][i] = -wdetJb * u_normal * (dE + dP);
  }  // End Quadrature Point Loop
  return 0;
}

#endif  // blasius_h