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Flow_kernel.cu
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Flow_kernel.cu
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//////////////////////////////////////////////////////////////////////////////////
// //
//Copyright (C) 2018 Bosserelle //
// This code contains an adaptation of the St Venant equation from Basilisk //
// See //
// http://basilisk.fr/src/saint-venant.h and //
// S. Popinet. Quadtree-adaptive tsunami modelling. Ocean Dynamics, //
// doi: 61(9) : 1261 - 1285, 2011 //
// //
//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. //
// //
//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, see <http://www.gnu.org/licenses/>. //
//////////////////////////////////////////////////////////////////////////////////
// textures have to be declared here...
texture<float, 2, cudaReadModeElementType> texLZsBND;
texture<float, 2, cudaReadModeElementType> texRZsBND;
texture<float, 2, cudaReadModeElementType> texTZsBND;
texture<float, 2, cudaReadModeElementType> texBZsBND;
texture<float, 2, cudaReadModeElementType> texLUBND;
texture<float, 2, cudaReadModeElementType> texRUBND;
texture<float, 2, cudaReadModeElementType> texTUBND;
texture<float, 2, cudaReadModeElementType> texBUBND;
texture<float, 2, cudaReadModeElementType> texLVBND;
texture<float, 2, cudaReadModeElementType> texRVBND;
texture<float, 2, cudaReadModeElementType> texTVBND;
texture<float, 2, cudaReadModeElementType> texBVBND;
texture<float, 2, cudaReadModeElementType> texUWND;
texture<float, 2, cudaReadModeElementType> texVWND;
texture<float, 2, cudaReadModeElementType> texPATM;
texture<float, 2, cudaReadModeElementType> texRAIN;
template<class T>
struct SharedMemory
{
__device__ inline operator T *()
{
extern __shared__ int __smem[];
return (T *)__smem;
}
__device__ inline operator const T *() const
{
extern __shared__ int __smem[];
return (T *)__smem;
}
};
// specialize for double to avoid unaligned memory
// access compile errors
template<>
struct SharedMemory<double>
{
__device__ inline operator double *()
{
extern __shared__ double __smem_d[];
return (double *)__smem_d;
}
__device__ inline operator const double *() const
{
extern __shared__ double __smem_d[];
return (double *)__smem_d;
}
};
template<class T>
__device__ T sq(T a)
{
return a*a;
}
__device__ int findleftG(int ix,int iy,int leftblk, int ibl, int bdimx)
{
int ileft;
if (ix == 0)
{
if (leftblk != ibl)
{
ileft = 15 + iy * bdimx + leftblk * (bdimx*bdimx);
}
else
{
ileft = 0 + iy * bdimx + ibl*(bdimx*bdimx);
}
}
else
{
ileft=(ix-1) + iy * bdimx + ibl*(bdimx*bdimx);
}
return ileft;
}
__device__ int findleftGSM(int ix, int iy, int leftblk, int ibl, int bdimx)
{
int ileft;
if (leftblk != ibl)
{
ileft = 15 + iy * bdimx + leftblk * (bdimx*bdimx);
}
else
{
ileft = 0 + iy * bdimx + ibl*(bdimx*bdimx);
}
return ileft;
}
__device__ int findrightG(int ix,int iy, int rightblk, int ibl, int bdimx)
{
int iright;
if (ix == (bdimx-1))
{
if (rightblk != ibl)
{
iright = 0 + iy * bdimx + rightblk * (bdimx*bdimx);
}
else
{
iright = 15 + iy * bdimx + ibl*(bdimx*bdimx);
}
}
else
{
iright = (ix+1) + iy * bdimx + ibl*(bdimx*bdimx);
}
return iright;
}
__device__ int findrightGSM(int ix, int iy, int rightblk, int ibl, int bdimx)
{
int iright;
if (rightblk != ibl)
{
iright = 0 + iy * bdimx + rightblk * (bdimx*bdimx);
}
else
{
iright = 15 + iy * bdimx + ibl*(bdimx*bdimx);
}
return iright;
}
__device__ int findtopG(int ix,int iy, int topblk, int ibl, int bdimx)
{
int itop;
if (iy == (bdimx - 1))
{
if (topblk != ibl)// if it not refering to itself it has top neighbour
{
itop = ix + 0 * bdimx + topblk * (bdimx*bdimx);
}
else
{
itop = ix + 15 * bdimx + ibl*(bdimx*bdimx);
}
}
else
{
itop = ix + (iy+1) * bdimx + ibl*(bdimx*bdimx);
}
return itop;
}
__device__ int findtopGSM(int ix, int iy, int topblk, int ibl, int bdimx)
{
int itop;
if (topblk != ibl)
{
itop = ix + 0 * bdimx + topblk * (bdimx*bdimx);
}
else
{
itop = ix + 15 * bdimx + ibl*(bdimx*bdimx);
}
return itop;
}
__device__ int findbotG(int ix,int iy, int botblk, int ibl, int bdimx)
{
int ibot;
if (iy == 0)
{
if (botblk != ibl)
{
ibot = ix + 15 * bdimx + botblk * (bdimx*bdimx);
}
else
{
ibot = ix + 0 * bdimx + ibl*(bdimx*bdimx);
}
}
else
{
ibot = ix + (iy-1) * bdimx + ibl*(bdimx*bdimx);
}
return ibot;
}
__device__ int findbotGSM(int ix, int iy, int botblk, int ibl, int bdimx)
{
int ibot;
if (botblk != ibl)
{
ibot = ix + 15 * bdimx + botblk * (bdimx*bdimx);
}
else
{
ibot = ix + 0 * bdimx + ibl*(bdimx*bdimx);
}
return ibot;
}
__device__ float minmod2fGPU(float theta,float s0, float s1, float s2)
{
//theta should be used as a global var
// can be used to tune the limiting (theta=1
//gives minmod, the most dissipative limiter and theta = 2 gives
// superbee, the least dissipative).
//float theta = 1.3f;
if (s0 < s1 && s1 < s2) {
float d1 = theta*(s1 - s0);
float d2 = (s2 - s0) / 2.0f;
float d3 = theta*(s2 - s1);
if (d2 < d1) d1 = d2;
return min(d1, d3);
}
if (s0 > s1 && s1 > s2) {
float d1 = theta*(s1 - s0), d2 = (s2 - s0) / 2.0f, d3 = theta*(s2 - s1);
if (d2 > d1) d1 = d2;
return max(d1, d3);
}
return 0.;
}
template <class T> __host__ __device__ T minmod2GPU(T theta, T s0, T s1, T s2)
{
//theta should be used as a global var
// can be used to tune the limiting (theta=1
//gives minmod, the most dissipative limiter and theta = 2 gives
// superbee, the least dissipative).
//float theta = 1.3f;
if (s0 < s1 && s1 < s2) {
T d1 = theta*(s1 - s0);
T d2 = (s2 - s0) / T(2.0);
T d3 = theta*(s2 - s1);
if (d2 < d1) d1 = d2;
return min(d1, d3);
}
if (s0 > s1 && s1 > s2) {
T d1 = theta*(s1 - s0), d2 = (s2 - s0) / T(2.0), d3 = theta*(s2 - s1);
if (d2 > d1) d1 = d2;
return max(d1, d3);
}
return T(0.0);
}
template <class T> __global__ void gradientGPUXY(int nx, int ny, T theta, T delta, T *a, T *dadx, T *dady)
{
//
int ix = blockIdx.x*blockDim.x + threadIdx.x;
int iy = blockIdx.y*blockDim.y + threadIdx.y;
//int tx = threadIdx.x;
//int ty = threadIdx.y;
int i = ix + iy*nx;
int xplus, yplus, xminus, yminus;
T a_i,a_r, a_l, a_t, a_b;
//__shared__ float a_s[18][18];
if (ix < nx && iy < ny)
{
xplus = min(ix + 1, nx - 1);
xminus = max(ix - 1, 0);
yplus = min(iy + 1, ny - 1);
yminus = max(iy - 1, 0);
/*
a_s[tx + 1][ty + 1] = a[ix + iy*nx];
__syncthreads;
// read the halo around the tile
if (threadIdx.x == blockDim.x - 1)
a_s[tx + 2][ty + 1] = a[xplus + iy*nx];
if (threadIdx.x == 0)
a_s[tx][ty + 1] = a[xminus + iy*nx];
if (threadIdx.y == blockDim.y - 1)
a_s[tx + 1][ty + 2] = a[ix + yplus*nx];
if (threadIdx.y == 0)
a_s[tx + 1][ty] = a[ix + yminus*nx];
__syncthreads;
*/
a_i = a[ix + iy*nx];
a_r= a[xplus + iy*nx];
a_l= a[xminus + iy*nx];
a_t = a[ix + yplus*nx];
a_b = a[ix + yminus*nx];
//dadx[i] = minmod2fGPU(theta, a_s[tx][ty + 1], a_s[tx + 1][ty + 1], a_s[tx + 2][ty + 1]) / delta;
//dady[i] = minmod2fGPU(theta, a_s[tx + 1][ty], a_s[tx + 1][ty + 1], a_s[tx + 1][ty + 2]) / delta;
dadx[i] = minmod2GPU(theta, a_l, a_i, a_r) / delta;
dady[i] = minmod2GPU(theta, a_b, a_i, a_t) / delta;
}
}
template <class T> __global__ void gradientGPUXYBUQ(T theta, T delta, int *leftblk, int *rightblk, int* topblk, int * botblk, T *a, T *dadx, T *dady)
{
//int *leftblk,int *rightblk,int* topblk, int * botblk,
//int ix = threadIdx.x+1;
//int iy = threadIdx.y+1;
int ix = threadIdx.x;
int iy = threadIdx.y;
int ibl = blockIdx.x;
int i = ix + iy * blockDim.x + ibl*(blockDim.x*blockDim.y);
int ileft, iright, itop, ibot;
ileft = findleftG(ix,iy, leftblk[ibl], ibl, blockDim.x);
iright = findrightG(ix,iy, rightblk[ibl], ibl, blockDim.x);
itop = findtopG(ix,iy, topblk[ibl], ibl, blockDim.x);
ibot = findbotG(ix,iy, botblk[ibl], ibl, blockDim.x);
/*
if (blockIdx.x == 0 && threadIdx.x == 0 && threadIdx.y == 0)
{
printf("i= %i\t ileft=%i\t iright=%i\t itop=%i\t ibot=%i\n", i,ileft,iright,itop,ibot);
}
*/
T a_i, a_r, a_l, a_t, a_b;
/*
__shared__ float a_s[18][18];
a_s[ix][iy] = a[i];
__syncthreads;
//syncthread is needed here ?
// read the halo around the tile
if (threadIdx.x == blockDim.x - 1)
a_s[ix + 1][iy] = a[iright];
if (threadIdx.x == 0)
a_s[ix-1][iy] = a[ileft];
if (threadIdx.y == blockDim.y - 1)
a_s[ix ][iy + 1] = a[itop];
if (threadIdx.y == 0)
a_s[ix ][iy-1] = a[ibot];
__syncthreads;
*/
a_i = a[i];
a_r = a[iright];
a_l = a[ileft];
a_t = a[itop];
a_b = a[ibot];
/*
dadx[i] = minmod2GPU(theta, a_s[ix-1][iy], a_s[ix][iy], a_s[ix + 1][iy]) / delta;
dady[i] = minmod2GPU(theta, a_s[ix][iy-1], a_s[ix][iy], a_s[ix][iy + 1]) / delta;
*/
dadx[i] = minmod2GPU(theta, a_l, a_i, a_r) / delta;
dady[i] = minmod2GPU(theta, a_b, a_i, a_t) / delta;
}
template <class T> __global__ void gradientGPUXYBUQSM(T theta, T delta, int *leftblk, int *rightblk, int* topblk, int * botblk, T *a, T *dadx, T *dady)
{
//int *leftblk,int *rightblk,int* topblk, int * botblk,
//int ix = threadIdx.x+1;
//int iy = threadIdx.y+1;
int ix = threadIdx.x;
int iy = threadIdx.y;
int ibl = blockIdx.x;
// shared array index to make the code bit more readable
int sx = ix + 1;
int sy = iy + 1;
int i = ix + iy * blockDim.x + ibl*(blockDim.x*blockDim.y);
int ileft, iright, itop, ibot;
/*
if (blockIdx.x == 0 && threadIdx.x == 0 && threadIdx.y == 0)
{
printf("i= %i\t ileft=%i\t iright=%i\t itop=%i\t ibot=%i\n", i,ileft,iright,itop,ibot);
}
*/
//T a_i, a_r, a_l, a_t, a_b;
__shared__ T a_s[18][18];
a_s[sx][sy] = a[i];
//__syncthreads;
//syncthread is needed here ?
// read the halo around the tile
if (threadIdx.x == blockDim.x - 1)
{
iright = findrightGSM(ix, iy, rightblk[ibl], ibl, blockDim.x);
a_s[sx + 1][sy] = a[iright];
}
if (threadIdx.x == 0)
{
ileft = findleftGSM(ix, iy, leftblk[ibl], ibl, blockDim.x);
a_s[sx-1][sy] = a[ileft];
}
if (threadIdx.y == blockDim.y - 1)
{
itop = findtopGSM(ix, iy, topblk[ibl], ibl, blockDim.x);
a_s[sx][sy + 1] = a[itop];
}
if (threadIdx.y == 0)
{
ibot = findbotGSM(ix, iy, botblk[ibl], ibl, blockDim.x);
a_s[sx][sy - 1] = a[ibot];
}
__syncthreads;
/*
a_i = a[i];
a_r = a[iright];
a_l = a[ileft];
a_t = a[itop];
a_b = a[ibot];
*/
dadx[i] = minmod2GPU(theta, a_s[sx-1][sy], a_s[sx][sy], a_s[sx + 1][sy]) / delta;
dady[i] = minmod2GPU(theta, a_s[sx][sy-1], a_s[sx][sy], a_s[sx][sy + 1]) / delta;
/*
dadx[i] = minmod2GPU(theta, a_l, a_i, a_r) / delta;
dady[i] = minmod2GPU(theta, a_b, a_i, a_t) / delta;
*/
}
template <class T>
__global__ void interp2ATMP(float xoatm,float yoatm,float dxatm,T delta, T Pref,T*blockxo, T *blockyo, T * P)
{
int ix = threadIdx.x;
int iy = threadIdx.y;
int ibl = blockIdx.x;
int i = ix + iy * blockDim.x + ibl*(blockDim.x*blockDim.y);
T x = blockxo[ibl] + ix*delta;
T y = blockyo[ibl] + iy*delta;
float Pw;
Pw = tex2D(texPATM, (x - xoatm) / dxatm + 0.5, (y - yoatm) / dxatm + 0.5);
P[i] = Pw - Pref;
}
__global__ void gradientGPUX(int nx, int ny,float theta, float delta, float *a, float *dadx)
{
int ix = blockIdx.x*blockDim.x + threadIdx.x;
int iy = blockIdx.y*blockDim.y + threadIdx.y;
int tx = threadIdx.x;
int ty = threadIdx.y;
int i = ix + iy*nx;
int xplus, xminus;
__shared__ float a_s[16][16]; // Hard wired stuff Be carefull
__shared__ float al_s[16][16];
__shared__ float ar_s[16][16];
//float dadxi;
if (ix < nx && iy < ny)
{
//
//
xplus = min(ix + 1, nx - 1);
xminus = max(ix - 1, 0);
i = ix + iy*nx;
//a_s[tx][ty] = a[ix + iy*nx];
//al_s[tx][ty] = a[xminus + iy*nx];
//ar_s[tx][ty] = a[xplus + iy*nx];
a_s[tx][ty] = a[ix + iy*nx];
// read the halo around the tile
__syncthreads;
al_s[tx][ty] = a[xminus + iy*nx];
__syncthreads;
ar_s[tx][ty] = a[xplus + iy*nx];
// Need to wait for threadX 0 and threadX 16-1 to finish
__syncthreads;
//dadx[i] = (a[i] - a[xminus + iy*nx]) / delta;//minmod2(a[xminus+iy*nx], a[i], a[xplus+iy*nx]);
//dadx[i] = minmod2fGPU(theta,a[xminus + iy*nx], a[i], a[xplus + iy*nx]) / delta;
// These below are somewhat slower when using shared mem. I'm unsure why (bank conflict?)
//dadx[i] = minmod2fGPU(theta, al_s[tx][ty], a_s[tx][ty], ar_s[tx][ty]) / delta;
//dadx[i] = minmod2fGPU(theta, a_s[tx][ty], a_s[tx+1][ty], a_s[tx+2][ty]) / delta;
//__device__ float minmod2fGPU(float theta,float s0, float s1, float s2)
//float d1, d2, d3;
//float s0, s1, s2;
//dadxi = 0.0f;
dadx[i] = minmod2fGPU(theta, al_s[tx][ty], a_s[tx][ty], ar_s[tx][ty]) / delta;
/*
s0 = al_s[tx][ty];// there will be bank conflict here
s1 = a_s[tx][ty];// there will be bank conflict here
s2 = ar_s[tx][ty];// there will be bank conflict here
if (s0 < s1 && s1 < s2) {
d1 = theta*(s1 - s0);
d2 = (s2 - s0) / 2.0f;
d3 = theta*(s2 - s1);
if (d2 < d1) d1 = d2;
dadxi = min(d1, d3);
}
if (s0 > s1 && s1 > s2) {
d1 = theta*(s1 - s0);
d2 = (s2 - s0) / 2.0f;
d3 = theta*(s2 - s1);
if (d2 > d1) d1 = d2;
dadxi = max(d1, d3);
}
dadx[i] = dadxi / delta;
*/
}
}
__global__ void gradientGPUXOLD(int nx, int ny, float theta, float delta, float *a, float *dadx)
{
int ix = blockIdx.x*blockDim.x + threadIdx.x;
int iy = blockIdx.y*blockDim.y + threadIdx.y;
int i = ix + iy*nx;
int xplus, xminus;
if (ix < nx && iy < ny)
{
//
//
xplus = min(ix + 1, nx - 1);
xminus = max(ix - 1, 0);
i = ix + iy*nx;
//dadx[i] = (a[i] - a[xminus + iy*nx]) / delta;//minmod2(a[xminus+iy*nx], a[i], a[xplus+iy*nx]);
dadx[i] = minmod2fGPU(theta, a[xminus + iy*nx], a[i], a[xplus + iy*nx]) / delta;
}
}
__global__ void gradientGPUYSM(int nx, int ny, float theta, float delta, float *a, float *dady)
{
int ix = blockIdx.x*blockDim.x + threadIdx.x;
int iy = blockIdx.y*blockDim.y + threadIdx.y;
int tx = threadIdx.x;
int ty = threadIdx.y;
int i = ix + iy*nx;
int yplus, yminus;
__shared__ float a_s[16][18];
float dadyi = 0.0f;
if (ix < nx && iy < ny)
{
//
//
yplus = min(iy + 1, ny - 1);
yminus = max(iy - 1, 0);
i = ix + iy*nx;
a_s[tx][ty] = a[ix + yminus*nx];
// read the halo around the tile
if (threadIdx.x == 15)//blockDim.x - 1
{
a_s[tx][ty + 1] = a[i];
a_s[tx][ty + 2] = a[ix + yplus*nx];
}
// Need to wait for threadX 0 and threadX 16-1 to finish
__syncthreads;
//dadx[i] = (a[i] - a[xminus + iy*nx]) / delta;//minmod2(a[xminus+iy*nx], a[i], a[xplus+iy*nx]);
//dady[i] = minmod2fGPU(theta, a[ix + yminus*nx], a[i], a[ix + yplus*nx]) / delta;
//dady[i] = minmod2fGPU(theta, a_s[tx][ty], a_s[tx][ty + 1], a_s[tx][ty + 2]) / delta;
float d1, d2, d3;
if (a_s[tx][ty] < a_s[tx][ty + 1] && a_s[tx][ty + 1] < a_s[tx][ty + 2]) {
d1 = theta*(a_s[tx][ty + 1] - a_s[tx][ty]);
d2 = (a_s[tx][ty + 2] - a_s[tx][ty]) / 2.0f;
d3 = theta*(a_s[tx][ty + 2] - a_s[tx][ty + 1]);
if (d2 < d1) d1 = d2;
dadyi = min(d1, d3);
}
if (a_s[tx][ty] > a_s[tx][ty + 1] && a_s[tx][ty + 1] > a_s[tx][ty + 2]) {
d1 = theta*(a_s[tx][ty + 1] - a_s[tx][ty]);
d2 = (a_s[tx][ty + 2] - a_s[tx][ty]) / 2.0f;
d3 = theta*(a_s[tx][ty + 2] - a_s[tx][ty + 1]);
if (d2 > d1) d1 = d2;
dadyi = max(d1, d3);
}
dady[i] = dadyi / delta;
}
}
__global__ void gradientGPUY(int nx, int ny,float theta, float delta, float *a, float *dady)
{
int ix = blockIdx.x*blockDim.x + threadIdx.x;
int iy = blockIdx.y*blockDim.y + threadIdx.y;
int i = ix + iy*nx;
int yplus, yminus;
if (ix < nx && iy < ny)
{
//
//
yplus = min(iy + 1, ny - 1);
yminus = max(iy - 1, 0);
i = ix + iy*nx;
//dadx[i] = (a[i] - a[xminus + iy*nx]) / delta;//minmod2(a[xminus+iy*nx], a[i], a[xplus+iy*nx]);
dady[i] = minmod2fGPU(theta,a[ix + yminus*nx], a[i], a[ix + yplus*nx]) / delta;
}
}
__global__ void updateKurgX( float delta, float g, float eps,float CFL, int *leftblk, float * hh, float *zs, float *uu, float * vv, float *dzsdx, float *dhdx, float * dudx, float *dvdx, float *Fhu, float *Fqux, float *Fqvx, float *Su, float * dtmax)
{
int ix = threadIdx.x;
int iy = threadIdx.y;
int ibl = blockIdx.x;
//float epsc = 0.07f;
// This is based on kurganov and Petrova 2007
int i = ix + iy * blockDim.x + ibl*(blockDim.x*blockDim.y);
int ileft;
ileft = findleftG(ix, iy, leftblk[ibl], ibl, blockDim.x);
//iright = findrightG(ix, iy, rightblk[ibl], ibl, blockDim.x);
//itop = findtopG(ix, iy, topblk[ibl], ibl, blockDim.x);
//ibot = findbotG(ix, iy, botblk[ibl], ibl, blockDim.x);
//if (ix < nx && iy < ny)
{
//xplus = min(ix + 1, nx - 1);
//xminus = max(ix - 1, 0);
//yplus = min(iy + 1, ny - 1);
//yminus = max(iy - 1, 0);
float dhdxi= dhdx[i];
float dhdxmin = dhdx[ileft];
float cm = 1.0f;// 0.1;
float fmu = 1.0f;
//float fmv = 1.0;
//__shared__ float hi[16][16];
float hi = hh[i];
float hn = hh[ileft];
if (hi > eps || hn > eps)
{
float dx, zi, zl, zn, zr, zlr, hl, up, hp, hr, um, hm,sl,sr;
// along X
dx = delta*0.5f;
zi = zs[i] - hi;
//printf("%f\n", zi);
//zl = zi - dx*(dzsdx[i] - dhdx[i]);
zl = zi - dx*(dzsdx[i] - dhdxi);
//printf("%f\n", zl);
zn = zs[ileft] - hn;
//printf("%f\n", zn);
zr = zn + dx*(dzsdx[ileft] - dhdxmin);
zlr = max(zl, zr);
//hl = hi - dx*dhdx[i];
hl = hi - dx*dhdxi;
up = uu[i] - dx*dudx[i];
hp = max(0.0f, hl + zl - zlr);
hr = hn + dx*dhdxmin;
um = uu[ileft] + dx*dudx[ileft];
hm = max(0.0f, hr + zr - zlr);
float fh, fu, fv;
//float dtmaxf = 1 / 1e-30f;
//We can now call one of the approximate Riemann solvers to get the fluxes.
float cp, cmo, ap, am, qm, qp, a, dlt, ad, hm2, hp2, ga,apm;
float epsi = 1e-30f;
cp = sqrtf(g*hp);
cmo = sqrtf(g*hm);
ap = max(max(up + cp, um + cmo),0.0f);// eq. 2.22
//ap = max(ap, 0.0f);
am = min(min(up - cp, um - cmo),0.0f);//eq. 2.23
//am = min(am, 0.0f);
ad = 1.0f / (ap - am);
//Correct for spurious currents in really shallow depth
qm = hm*um;
qp = hp*up;
//qm = hm*um*(sqrtf(2) / sqrtf(1.0f + max(1.0f, powf(epsc / hm,4.0f))));
//qp = hp*up*(sqrtf(2) / sqrtf(1.0f + max(1.0f, powf(epsc / hp,4.0f))));
a = max(ap, -am);
dlt = delta*cm / fmu;
hm2 = sq(hm);
hp2 = sq(hp);
ga = g*0.5f;
apm = ap*am;
if (a > epsi)
{
fh = (ap*qm - am*qp + apm*(hp - hm)) *ad; // H in eq. 2.24 or eq 3.7 for F(h)
fu = (ap*(qm*um + ga*hm2 ) - am*(qp*up + ga*hp2 ) + apm*(qp - qm)) *ad; // Eq 3.7 second term (X direction)
//fu = (ap*(qm*um + g*sq(hm) / 2.0f) - am*(qp*up + g*sq(hp) / 2.0f) + ap*am*(qp - qm)) / (ap - am);
float dt = CFL*dlt / a;
if (dt < dtmax[i])
{
dtmax[i] = dt;
}
// *dtmax = dt;
}
else
{
fh = 0.0f;
fu = 0.0f;
dtmax[i] = 1.0f / 1e-30f;
}
//kurganovf(hm, hp, um, up, delta*cm / fmu, &fh, &fu, &dtmaxf);
/*
void kurganovf(float hm, float hp, float um, float up, float Delta, float * fh, float * fq, float * dtmax)
float eps = epsilon;
float cp = sqrtf(g*hp), cm = sqrtf(g*hm);
float ap = max(up + cp, um + cm); ap = max(ap, 0.0f);
float am = min(up - cp, um - cm); am = min(am, 0.0f);
float qm = hm*um, qp = hp*up;
float a = max(ap, -am);
if (a > eps) {
*fh = (ap*qm - am*qp + ap*am*(hp - hm)) / (ap - am); // (4.5) of [1]
*fq = (ap*(qm*um + g*sq(hm) / 2.) - am*(qp*up + g*sq(hp) / 2.) +
ap*am*(qp - qm)) / (ap - am);
float dt = CFL*Delta / a;
if (dt < *dtmax)
*dtmax = dt;
}
else
*fh = *fq = 0.;*/
if (fh > 0.0f)
{
fv = (vv[ileft] + dx*dvdx[ileft])*fh;// Eq 3.7 third term? (X direction)
}
else
{
fv = (vv[i] - dx*dvdx[i])*fh;
}
//fv = (fh > 0.f ? vv[xminus + iy*nx] + dx*dvdx[xminus + iy*nx] : vv[i] - dx*dvdx[i])*fh;
//dtmax needs to be stored in an array and reduced at the end
//dtmax = dtmaxf;
//dtmaxtmp = min(dtmax, dtmaxtmp);
/*if (ix == 11 && iy == 0)
{
printf("a=%f\t b=%f\t c=%f\t d=%f\n", ap*(qm*um + ga*hm2), -am*(qp*up + ga*hp2),( ap*(qm*um + g*sq(hm) / 2.0f) - am*(qp*up + g*sq(hp) / 2.0f) + ap*am*(qp - qm) ) *ad/100.0f, ad);
}
*/
/*
#### Topographic source term
In the case of adaptive refinement, care must be taken to ensure
well-balancing at coarse/fine faces (see [notes/balanced.tm]()). */
sl = ga*(hp2 - sq(hl) + (hl + hi)*(zi - zl));
sr = ga*(hm2 - sq(hr) + (hr + hn)*(zn - zr));
////Flux update
Fhu[i] = fmu * fh;
Fqux[i] = fmu * (fu - sl);
Su[i] = fmu * (fu - sr);
Fqvx[i] = fmu * fv;
}
else
{
dtmax[i] = 1.0f / 1e-30f;
Fhu[i] = 0.0f;
Fqux[i] = 0.0f;
Su[i] = 0.0f;
Fqvx[i] = 0.0f;
}
}
}
template <class T>
__global__ void updateKurgXATM(T delta, T g, T eps, T CFL, T Pa2m, int *leftblk, T * hh, T *zs, T *uu, T * vv, T *Patm, T *dzsdx, T *dhdx, T * dudx, T *dvdx, T *dpdx, T *Fhu, T *Fqux, T *Fqvx, T *Su, T * dtmax)
{
int ix = threadIdx.x;
int iy = threadIdx.y;
int ibl = blockIdx.x;
int i = ix + iy * blockDim.x + ibl*(blockDim.x*blockDim.y);
int ileft;
ileft = findleftG(ix, iy, leftblk[ibl], ibl, blockDim.x);
//iright = findrightG(ix, iy, rightblk[ibl], ibl, blockDim.x);
//itop = findtopG(ix, iy, topblk[ibl], ibl, blockDim.x);
//ibot = findbotG(ix, iy, botblk[ibl], ibl, blockDim.x);
//if (ix < nx && iy < ny)
{
//xplus = min(ix + 1, nx - 1);
//xminus = max(ix - 1, 0);
//yplus = min(iy + 1, ny - 1);
//yminus = max(iy - 1, 0);
T dhdxi = dhdx[i];
T dhdxmin = dhdx[ileft];
T cm = (T)1.0;// 0.1;
T fmu = (T)1.0;
//float fmv = 1.0;
//__shared__ float hi[16][16];
T hi = hh[i];
T hn = hh[ileft];
if (hi > eps || hn > eps)
{
T dx, zi, zl, zn, zr, zlr, hl, up, hp, hr, um, hm, sl, sr;
// along X
dx = delta*T(0.5);
zi = zs[i] - hi + Pa2m * Patm[i];
//printf("%f\n", zi);
//zl = zi - dx*(dzsdx[i] - dhdx[i]);
zl = zi - dx*(dzsdx[i] - dhdxi + Pa2m*dpdx[i]);
//printf("%f\n", zl);
zn = zs[ileft] - hn + Pa2m * Patm[ileft];
//printf("%f\n", zn);
zr = zn + dx*(dzsdx[ileft] - dhdxmin + Pa2m*dpdx[ileft]);
zlr = max(zl, zr);
//hl = hi - dx*dhdx[i];
hl = hi - dx*dhdxi;
up = uu[i] - dx*dudx[i];
hp = max((T)0.0, hl + zl - zlr);
hr = hn + dx*dhdxmin;
um = uu[ileft] + dx*dudx[ileft];
hm = max((T)0.0, hr + zr - zlr);
T fh, fu, fv;
//float dtmaxf = 1 / 1e-30f;
//We can now call one of the approximate Riemann solvers to get the fluxes.
T cp, cmo, ap, am, qm, qp, a, dlt, ad, hm2, hp2, ga, apm;
T epsi = (T)1e-30;
//T epsc = T(0.07);
cp = sqrtf(g*hp);
cmo = sqrtf(g*hm);
ap = max(max(up + cp, um + cmo), (T)0.0);
//ap = max(ap, 0.0f);