refactor(meshGeneration): working on gmsh to generate curvilinear isogeomatric spherical mesh

utils/meshGeneration/sphere.geo

@@ -0,0 +1,38 @@
+SetFactory("OpenCASCADE");
+
+// Define parameters - these can be overridden from the command line
+// using the -setnumber flag, e.g., gmsh sphere.geo -setnumber Parameters/Order 2
+DefineConstant[
+  radius = {1.0, Name "Parameters/Radius"},
+  coreRes = {0.01, Name "Parameters/CoreRes"},
+  outerRes = {0.1, Name "Parameters/OuterRes"},
+  kVal = {2.0, Name "Parameters/K"},
+  order = {2, Name "Parameters/Order"} // Mesh element order
+];
+
+// Define Geometry
+Sphere(1) = {0, 0, 0, radius};
+
+Physical Volume("sphere_volume", 1) = {1}; // Tag the volume
+
+// Define variable mesh size using a MathEval Field
+// Field Formula: a + (b-a) * (1 - Exp(-k*r))
+// Need to handle r=0 case for Sqrt and Exp
+Field[1] = MathEval;
+Field[1].F = Sprintf("%.15g + (%.15g - %.15g) * (1 - Exp(-%.15g * Max(Sqrt(x*x+y*y+z*z), 1e-9)))", coreRes, outerRes, coreRes, kVal);
+
+// Use this field as the background mesh size field
+Background Field = 1;
+
+// Set Mesh Options
+Mesh.ElementOrder = order; // Set the mesh order (1=linear, 2=quadratic, etc.)
+
+// Optional: Optimize high-order elements for better quality
+// Mesh.HighOrderOptimize = 1;
+
+// Optional: Choose 3D meshing algorithm if default isn't good (e.g., 1=MeshAdapt, 4=Frontal, 5=Delaunay, 6=Frontal-Delaunay, 7=MMG3D)
+// Mesh.Algorithm3D = 7;
+
+// Define Physical Groups (optional but good practice)
+// Physical Volume("sphere_volume", 1) = {1}; // Tag the volume
+// Physical Surface("sphere_surface", 2) = {1}; // Tag the boundary surface