First pass at core GR infrastructure

zero/gkyl_eqn_type.h

@@ -12,6 +12,7 @@ enum gkyl_eqn_type {
   GKYL_EQN_MHD,  // Ideal MHD equations
   GKYL_EQN_BURGERS, // Burgers equations
   GKYL_EQN_ADVECTION, // Scalar advection equation
+  GKYL_EQN_GR_EULER, // General relativistic Euler equations.
 };
 
 // Identifiers for specific field object types

zero/gkyl_gr_spacetime_diff.h

@@ -0,0 +1,265 @@
+#pragma once
+
+#include <math.h>
+#include <gkyl_array.h>
+#include <gkyl_gr_spacetime.h>
+#include <gkyl_range.h>
+#include <gkyl_util.h>
+
+/**
+* Compute the rank-3 (spatial) partial derivative of the spatial metric tensor at a given point in spacetime, using finite differences.
+*
+* @param spacetime Base spacetime object.
+* @param t Time coordinate.
+* @param x Spatial coordinate (x-direction).
+* @param y Spatial coordinate (y-direction).
+* @param z Spatial coordinate (z-direction).
+* @param dx Spatial coordinate spacing (x-direction).
+* @param dy Spatial coordinate spacing (y-direction).
+* @param dz Spatial coordinate spacing (z-direction).
+* @param spatial_metric_tensor_diff Rank-3 partial derivative of the spatial metric tensor (output).
+*/
+GKYL_CU_D
+void
+gkyl_gr_spatial_metric_tensor_diff(const struct gkyl_gr_spacetime* spacetime, const double t, const double x, const double y, const double z,
+  const double dx, const double dy, const double dz, double**** spatial_metric_tensor_diff);
+
+/**
+* Compute the rank-3 (spacetime) partial derivative of the spacetime metric tensor at a given point in spacetime, using finite differences.
+*
+* @param spacetime Base spacetime object.
+* @param t Time coordinate.
+* @param x Spatial coordinate (x-direction).
+* @param y Spatial coordinate (y-direction).
+* @param z Spatial coordinate (z-direction).
+* @param dt Time coordinate spacing.
+* @param dx Spatial coordinate spacing (x-direction).
+* @param dy Spatial coordinate spacing (y-direction).
+* @param dz Spatial coordinate spacing (z-direction).
+* @param spacetime_metric_tensor_diff Rank-3 partial derivative of the spacetime metric tensor (output).
+*/
+GKYL_CU_D
+void
+gkyl_gr_spacetime_metric_tensor_diff(const struct gkyl_gr_spacetime* spacetime, const double t, const double x, const double y, const double z,
+  const double dt, const double dx, const double dy, const double dz, double**** spacetime_metric_tensor_diff);
+
+/**
+* Compute the rank-1 (spatial) partial derivative of the lapse function at a given point in spacetime, using finite differences.
+*
+* @param spacetime Base spacetime object.
+* @param t Time coordinate.
+* @param x Spatial coordinate (x-direction).
+* @param y Spatial coordinate (y-direction).
+* @param z Spatial coordinate (z-direction).
+* @param dx Spatial coordinate spacing (x-direction).
+* @param dy Spatial coordinate spacing (y-direction).
+* @param dz Spatial coordinate spacing (z-direction).
+* @param lapse_function_diff Rank-1 partial derivative of the lapse function (output).
+*/
+GKYL_CU_D
+void
+gkyl_gr_lapse_function_diff(const struct gkyl_gr_spacetime* spacetime, const double t, const double x, const double y, const double z,
+  const double dx, const double dy, const double dz, double** lapse_function_diff);
+
+/**
+* Compute the rank-2 (spatial) partial derivative of the shift vector at a given point in spacetime, using finite differences.
+*
+* @param spacetime Base spacetime object.
+* @param t Time coordinate.
+* @param x Spatial coordinate (x-direction).
+* @param y Spatial coordinate (y-direction).
+* @param z Spatial coordinate (z-direction).
+* @param dx Spatial coordinate spacing (x-direction).
+* @param dy Spatial coordinate spacing (y-direction).
+* @param dz Spatial coordinate spacing (z-direction).
+* @param shift_vector_diff Rank-2 partial derivative of the shift vector (output).
+*/
+GKYL_CU_D
+void
+gkyl_gr_shift_vector_diff(const struct gkyl_gr_spacetime* spacetime, const double t, const double x, const double y, const double z,
+  const double dx, const double dy, const double dz, double*** shift_vector_diff);
+
+/**
+* Compute the rank-3 (spatial) Christoffel symbols at a given point in spacetime, using finite differences.
+*
+* @param spacetime Base spacetime object.
+* @param t Time coordinate.
+* @param x Spatial coordinate (x-direction).
+* @param y Spatial coordinate (y-direction).
+* @param z Spatial coordinate (z-direction).
+* @param dx Spatial coordinate spacing (x-direction).
+* @param dy Spatial coordinate spacing (y-direction).
+* @param dz Spatial coordinate spacing (z-direction).
+* @param spatial_christoffel Rank-3 spatial Christoffel symbols (output).
+*/
+GKYL_CU_D
+void
+gkyl_gr_spatial_christoffel_fd(const struct gkyl_gr_spacetime* spacetime, const double t, const double x, const double y, const double z,
+  const double dx, const double dy, const double dz, double**** spatial_christoffel);
+
+/**
+* Compute the rank-3 (spacetime) Christoffel symbols at a given point in spacetime, using finite differences.
+*
+* @param spacetime Base spacetime object.
+* @param t Time coordinate.
+* @param x Spatial coordinate (x-direction).
+* @param y Spatial coordinate (y-direction).
+* @param z Spatial coordinate (z-direction).
+* @param dt Time coordinate spacing.
+* @param dx Spatial coordinate spacing (x-direction).
+* @param dy Spatial coordinate spacing (y-direction).
+* @param dz Spatial coordinate spacing (z-direction).
+* @param spacetime_christoffel Rank-3 spacetime Christoffel symbols (output).
+*/
+GKYL_CU_D
+void
+gkyl_gr_spacetime_christoffel_fd(const struct gkyl_gr_spacetime* spacetime, const double t, const double x, const double y, const double z,
+  const double dt, const double dx, const double dy, const double dz, double**** spacetime_christoffel);
+
+/**
+* Compute the rank-4 (spatial) Riemann curvature tensor at a given point in spacetime, using finite differences.
+*
+* @param spacetime Base spacetime object.
+* @param t Time coordinate.
+* @param x Spatial coordinate (x-direction).
+* @param y Spatial coordinate (y-direction).
+* @param z Spatial coordinate (z-direction).
+* @param dx Spatial coordinate spacing (x-direction).
+* @param dy Spatial coordinate spacing (y-direction).
+* @param dz Spatial coordinate spacing (z-direction).
+* @param spatial_riemann_tensor Rank-4 spatial Riemann curvature tensor (output).
+*/
+GKYL_CU_D
+void
+gkyl_gr_spatial_riemann_tensor_fd(const struct gkyl_gr_spacetime* spacetime, const double t, const double x, const double y, const double z,
+  const double dx, const double dy, const double dz, double***** spatial_riemann_tensor);
+
+/**
+* Compute the rank-4 (spacetime) Riemann curvature tensor at a given point in spacetime, using finite differences.
+*
+* @param spacetime Base spacetime object.
+* @param t Time coordinate.
+* @param x Spatial coordinate (x-direction).
+* @param y Spatial coordinate (y-direction).
+* @param z Spatial coordinate (z-direction).
+* @param dt Time coordinate spacing.
+* @param dx Spatial coordinate spacing (x-direction).
+* @param dy Spatial coordinate spacing (y-direction).
+* @param dz Spatial coordinate spacing (z-direction).
+* @param spacetime_riemann_tensor Rank-4 spacetime Riemann curvature tensor (output).
+*/
+GKYL_CU_D
+void
+gkyl_gr_spacetime_riemann_tensor_fd(const struct gkyl_gr_spacetime* spacetime, const double t, const double x, const double y, const double z,
+  const double dt, const double dx, const double dy, const double dz, double***** spacetime_riemann_tensor);
+
+/**
+* Compute the rank-2 (spatial) Ricci curvature tensor at a given point in spacetime, using finite differences.
+*
+* @param spacetime Base spacetime object.
+* @param t Time coordinate.
+* @param x Spatial coordinate (x-direction).
+* @param y Spatial coordinate (y-direction).
+* @param z Spatial coordinate (z-direction).
+* @param dx Spatial coordinate spacing (x-direction).
+* @param dy Spatial coordinate spacing (y-direction).
+* @param dz Spatial coordinate spacing (z-direction).
+* @param spatial_ricci_tensor Rank-2 spatial Ricci curvature tensor (output).
+*/
+GKYL_CU_D
+void
+gkyl_gr_spatial_ricci_tensor_fd(const struct gkyl_gr_spacetime* spacetime, const double t, const double x, const double y, const double z,
+  const double dx, const double dy, const double dz, double*** spatial_ricci_tensor);
+
+/**
+* Compute the rank-2 (spacetime) Ricci curvature tensor at a given point in spacetime, using finite differences.
+*
+* @param spacetime Base spacetime object.
+* @param t Time coordinate.
+* @param x Spatial coordinate (x-direction).
+* @param y Spatial coordinate (y-direction).
+* @param z Spatial coordinate (z-direction).
+* @param dt Time coordinate spacing.
+* @param dx Spatial coordinate spacing (x-direction).
+* @param dy Spatial coordinate spacing (y-direction).
+* @param dz Spatial coordinate spacing (z-direction).
+* @param spacetime_ricci_tensor Rank-2 spacetime Ricci curvature tensor (output).
+*/
+GKYL_CU_D
+void
+gkyl_gr_spacetime_ricci_tensor_fd(const struct gkyl_gr_spacetime* spacetime, const double t, const double x, const double y, const double z,
+  const double dt, const double dx, const double dy, const double dz, double*** spacetime_ricci_tensor);
+
+/**
+* Compute the (spatial) Ricci scalar curvature at a given point in spacetime, using finite differences.
+*
+* @param spacetime Base spacetime object.
+* @param t Time coordinate.
+* @param x Spatial coordinate (x-direction).
+* @param y Spatial coordinate (y-direction).
+* @param z Spatial coordinate (z-direction).
+* @param dx Spatial coordinate spacing (x-direction).
+* @param dy Spatial coordinate spacing (y-direction).
+* @param dz Spatial coordinate spacing (z-direction).
+* @param spatial_ricci_scalar Spatial Ricci scalar curvature (output).
+*/
+GKYL_CU_D
+void
+gkyl_gr_spatial_ricci_scalar_fd(const struct gkyl_gr_spacetime* spacetime, const double t, const double x, const double y, const double z,
+  const double dx, const double dy, const double dz, double* spatial_ricci_scalar);
+
+/**
+* Compute the (spacetime) Ricci scalar curvature at a given point in spacetime, using finite differences.
+*
+* @param spacetime Base spacetime object.
+* @param t Time coordinate.
+* @param x Spatial coordinate (x-direction).
+* @param y Spatial coordinate (y-direction).
+* @param z Spatial coordinate (z-direction).
+* @param dt Time coordinate spacing.
+* @param dx Spatial coordinate spacing (x-direction).
+* @param dy Spatial coordinate spacing (y-direction).
+* @param dz Spatial coordinate spacing (z-direction).
+* @param spacetime_ricci_tensor Spacetime Ricci scalar curvature (output).
+*/
+GKYL_CU_D
+void
+gkyl_gr_spacetime_ricci_scalar_fd(const struct gkyl_gr_spacetime* spacetime, const double t, const double x, const double y, const double z,
+  const double dt, const double dx, const double dy, const double dz, double* spacetime_ricci_scalar);
+
+/**
+* Compute the rank-4 (spatial) Weyl curvature tensor at a given point in spacetime, using finite differences.
+*
+* @param spacetime Base spacetime object.
+* @param t Time coordinate.
+* @param x Spatial coordinate (x-direction).
+* @param y Spatial coordinate (y-direction).
+* @param z Spatial coordinate (z-direction).
+* @param dx Spatial coordinate spacing (x-direction).
+* @param dy Spatial coordinate spacing (y-direction).
+* @param dz Spatial coordinate spacing (z-direction).
+* @param spatial_weyl_tensor Rank-4 spatial Weyl curvature tensor (output).
+*/
+GKYL_CU_D
+void
+gkyl_gr_spatial_weyl_tensor_fd(const struct gkyl_gr_spacetime* spacetime, const double t, const double x, const double y, const double z,
+  const double dx, const double dy, const double dz, double***** spatial_weyl_tensor);
+
+/**
+* Compute the rank-4 (spacetime) Weyl curvature tensor at a given point in spacetime, using finite differences.
+*
+* @param spacetime Base spacetime object.
+* @param t Time coordinate.
+* @param x Spatial coordinate (x-direction).
+* @param y Spatial coordinate (y-direction).
+* @param z Spatial coordinate (z-direction).
+* @param dt Time coordinate spacing.
+* @param dx Spatial coordinate spacing (x-direction).
+* @param dy Spatial coordinate spacing (y-direction).
+* @param dz Spatial coordinate spacing (z-direction).
+* @param spacetime_weyl_tensor Rank-4 spacetime Weyl curvature tensor (output).
+*/
+GKYL_CU_D
+void
+gkyl_gr_spacetime_weyl_tensor_fd(const struct gkyl_gr_spacetime* spacetime, const double t, const double x, const double y, const double z,
+  const double dt, const double dx, const double dy, const double dz, double***** spacetime_weyl_tensor);

zero/gkyl_wv_gr_euler.h

@@ -0,0 +1,56 @@
+#pragma once
+
+#include <gkyl_wv_eqn.h>
+#include <gkyl_gr_spacetime.h>
+
+// Type of Riemann-solver to use:
+enum gkyl_wv_gr_euler_rp {
+  WV_GR_EULER_RP_LAX = 0, // Default (Lax fluxes).
+  WV_GR_EULER_RP_ROE,
+};
+
+// Input context, packaged as a struct.
+struct gkyl_wv_gr_euler_inp {
+  double gas_gamma; // Adiabatic index.
+  struct gkyl_gr_spacetime *spacetime; // Pointer to base spacetime object.
+  enum gkyl_wv_gr_euler_rp rp_type; // Type of Riemann-solver to use.
+  bool use_gpu; // Whether the wave equation object is on the host (false) or the device (true).
+};
+
+/**
+* Create a new general relativistic Euler equations object.
+*
+* @param gas_gamma Adiabatic index.
+* @param spacetime Pointer to base spacetime object.
+* @param use_gpu Whether the wave equation object is on the host (false) or the device (true).
+* @return Pointer to the general relativistic Euler equations object.
+*/
+struct gkyl_wv_eqn*
+gkyl_wv_gr_euler_new(double gas_gamma, struct gkyl_gr_spacetime* spacetime, bool use_gpu);
+
+/**
+* Create a new general relativistic Euler equations object, from an input context struct.
+*
+* @param inp Input context struct.
+* @return Pointer to the general relativistic Euler equations object.
+*/
+struct gkyl_wv_eqn*
+gkyl_wv_gr_euler_inew(const struct gkyl_wv_gr_euler_inp* inp);
+
+/**
+* Get adiabatic index.
+*
+* @param wv General relativistic Euler equations object.
+* @return Adiabatic index.
+*/
+double
+gkyl_wv_gr_euler_gas_gamma(const struct gkyl_wv_eqn* wv);
+
+/**
+* Get base spacetime object.
+*
+* @param wv General relativistic Euler equations object.
+* @return Pointer to the base spacetime object.
+*/
+struct gkyl_gr_spacetime*
+gkyl_wv_gr_euler_spacetime(const struct gkyl_wv_eqn* wv);