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+/* This file is part of the OpenLB library
+ *
+ * Copyright (C) 2006, 2007 Jonas Latt
+ * E-mail contact: info@openlb.net
+ * The most recent release of OpenLB can be downloaded at
+ * <http://www.openlb.net/>
+ *
+ * This program is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU General Public License
+ * as published by the Free Software Foundation; either version 2
+ * of the License, or (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public
+ * License along with this program; if not, write to the Free
+ * Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+ * Boston, MA 02110-1301, USA.
+*/
+
+/** \file
+ * Efficient 2D specializations for lbHelpersD2Q9.h
+ */
+#ifndef FIRST_ORDER_LB_HELPERS_2D_H
+#define FIRST_ORDER_LB_HELPERS_2D_H
+
+namespace olb {
+
+/// Compute Pi tensor efficiently on D2Q9 lattice
+namespace neqPiD2Q9 {
+
+using namespace olb::util::tensorIndices2D;
+
+template<typename T>
+T fromPiToFneq0(const T pi[3])
+{
+ return (T)2 * (-(T)1/(T)3*pi[xx] - (T)1/(T)3*pi[yy]);
+}
+
+template<typename T>
+T fromPiToFneq1(const T pi[3])
+{
+ return (T)1/(T)4 * ((T)1/(T)3*pi[xx] + (T)1/(T)3*pi[yy] - pi[xy]);
+}
+
+template<typename T>
+T fromPiToFneq2(const T pi[3])
+{
+ return (T)1/(T)2 * ((T)2/(T)3*pi[xx] - (T)1/(T)3*pi[yy]);
+}
+
+template<typename T>
+T fromPiToFneq3(const T pi[3])
+{
+ return (T)1/(T)4 * ((T)1/(T)3*pi[xx] + (T)1/(T)3*pi[yy] + pi[xy]);
+}
+
+template<typename T>
+T fromPiToFneq4(const T pi[3])
+{
+ return (T)1/(T)2 * (-(T)1/(T)3*pi[xx] + (T)2/(T)3*pi[yy]);
+}
+
+} // namespace neqPiD2Q9
+
+template<typename T>
+struct rlbHelpers<T, descriptors::D2Q9<>> {
+
+ static T rlbCollision (
+ Cell<T,descriptors::D2Q9<>>& cell,
+ T rho, const T u[2], const T pi[3], T omega )
+ {
+ typedef lbHelpers<T, descriptors::D2Q9<>> LH;
+ const T uSqr = u[0]*u[0] + u[1]*u[1];
+
+ cell[0] = LH::equilibrium(0, rho, u, uSqr) +
+ ((T)1-omega) * neqPiD2Q9::fromPiToFneq0(pi);
+ cell[1] = LH::equilibrium(1, rho, u, uSqr) +
+ ((T)1-omega) * neqPiD2Q9::fromPiToFneq1(pi);
+ cell[2] = LH::equilibrium(2, rho, u, uSqr) +
+ ((T)1-omega) * neqPiD2Q9::fromPiToFneq2(pi);
+ cell[3] = LH::equilibrium(3, rho, u, uSqr) +
+ ((T)1-omega) * neqPiD2Q9::fromPiToFneq3(pi);
+ cell[4] = LH::equilibrium(4, rho, u, uSqr) +
+ ((T)1-omega) * neqPiD2Q9::fromPiToFneq4(pi);
+ cell[5] = LH::equilibrium(5, rho, u, uSqr) +
+ ((T)1-omega) * neqPiD2Q9::fromPiToFneq1(pi);
+ cell[6] = LH::equilibrium(6, rho, u, uSqr) +
+ ((T)1-omega) * neqPiD2Q9::fromPiToFneq2(pi);
+ cell[7] = LH::equilibrium(7, rho, u, uSqr) +
+ ((T)1-omega) * neqPiD2Q9::fromPiToFneq3(pi);
+ cell[8] = LH::equilibrium(8, rho, u, uSqr) +
+ ((T)1-omega) * neqPiD2Q9::fromPiToFneq4(pi);
+ return uSqr;
+ }
+
+}; // struct rlbHelpers<D2Q9<>>
+
+} // namespace olb
+
+
+#endif